In cognitive radio networks,spectrum sensing under circumstances of dynamically varying noise and lacking prior information is a key challenge to the conventional spectrum sensing algorithms.Since the necessary inform...In cognitive radio networks,spectrum sensing under circumstances of dynamically varying noise and lacking prior information is a key challenge to the conventional spectrum sensing algorithms.Since the necessary information is rather difficult to obtain practically,most existing spectrum sensing methods are fettered in applications.Motivated by these,in this paper,a Frequency domain Goodness of Fit Test(FGoF)based spectrum sensing method is proposed.The FGoF makes full use of underlying information in Guard-Bands and the advantages of GoF test works for any distribution.Analytical and simulated results show that the FGoF is a robust spectrum sensing method in cognitive radio with the inherent advantages of invulnerability to dynamically varying noise.展开更多
The error distribution testing plays an important role in linear regression as distribution misspecification seriously affects the validity and efficiency of regression analysis. The least squares (OLS) residuals are ...The error distribution testing plays an important role in linear regression as distribution misspecification seriously affects the validity and efficiency of regression analysis. The least squares (OLS) residuals are often used to construct test statistics;in order to overcome the non-independent and identically residuals, the best linear unbiased scale (BLUS) residuals are applied in this paper, which, unlike OLS residuals, the residuals vector is identically and independently distributed. Based on the BLUS residuals, a new test statistic is constructed by using the sample random distance between sample quantile and quasi sample quantile derived from the null distribution, and the goodness-of-fit test of error distribution in the linear model is studied. The powers of the new tests under certain alternatives are examined. They are more powerful tests for the hypotheses concerned.展开更多
A new six-parameter continuous distribution called the Generalized Kumaraswamy Generalized Power Gompertz (GKGPG) distribution is proposed in this study, a graphical illustration of the probability density function an...A new six-parameter continuous distribution called the Generalized Kumaraswamy Generalized Power Gompertz (GKGPG) distribution is proposed in this study, a graphical illustration of the probability density function and cumulative distribution function is presented. The statistical features of the Generalized Kumaraswamy Generalized Power Gompertz distribution are systematically derived and adequately studied. The estimation of the model parameters in the absence of censoring and under-right censoring is performed using the method of maximum likelihood. The test statistic for right-censored data, criteria test for GKGPG distribution, estimated matrix Ŵ, Ĉ, and Ĝ, criteria test Y<sup>2</sup>n</sub>, alongside the quadratic form of the test statistic is derived. Mean simulated values of maximum likelihood estimates and their corresponding square mean errors are presented and confirmed to agree closely with the true parameter values. Simulated levels of significance for Y<sup>2</sup>n</sub> (γ) test for the GKGPG model against their theoretical values were recorded. We conclude that the null hypothesis for which simulated samples are fitted by GKGPG distribution is widely validated for the different levels of significance considered. From the summary of the results of the strength of a specific type of braided cord dataset on the GKGPG model, it is observed that the proposed GKGPG model fits the data set for a significance level ε = 0.05.展开更多
Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization an...Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.展开更多
Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization an...Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.展开更多
Hydrologic frequency analysis plays an important role in coastal and ocean engineering for structural design and disaster prevention in coastal areas. This paper proposes a Nonlinear Least Squares Method (NLSM), which...Hydrologic frequency analysis plays an important role in coastal and ocean engineering for structural design and disaster prevention in coastal areas. This paper proposes a Nonlinear Least Squares Method (NLSM), which estimates the three unknown parameters of the Weibull distribution simultaneously by an iteration method. Statistical test shows that the NLSM fits each data sample well. The effects of different parameter-fitting methods, distribution models, and threshold values are also discussed in the statistical analysis of storm set-down elevation. The best-fitting probability distribution is given and the corresponding return values are estimated for engineering design.展开更多
Confidence bands in a Normal Q-Q Plot allow us to detect non-normality of a data set rigorously, and in such a way that the conclusion does not depend on the subjectivity of the observer of the graph. In the construct...Confidence bands in a Normal Q-Q Plot allow us to detect non-normality of a data set rigorously, and in such a way that the conclusion does not depend on the subjectivity of the observer of the graph. In the construction of the graph, it is usual to fit a straight line to the plotted points, which serves both to check the hypothesis of normality (linear configuration of the plotted points) and to produce estimates of the parameters of the distribution. We can opt for dif-ferent types of lines. In this paper, we study the influence of five types of fitted straight lines in a Normal Q-Q Plot used for construction the confidence bands based on the exact distribution of the order statistics.展开更多
Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturall...Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturally follows. It is even more appropriate to have a model(s) with few predictor variables. This paper seeks to identify appropriate statistical distribution functions for fitting gold production in Ghana. The empirical paper relied mainly on quarterly secondary datasets on gold production between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Weibull, Log-Normal, Generalized Extreme Value (GEV) were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC, AICc and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the reduced modified 3-parameter Weibull distribution provided the best fit for gold production in Ghana. Though the reduced modified Weibull function is proposed, it is important however to recognize that other external factors can influence production levels. Also, the average quarterly fitted gold production is 1000334.8918 ± 75,327.080 (±7.5%) [i.e., 925,007.812 – 1,075,661.972]. This indicates that the average annually fitted gold production lies between 3700031.248 and 4302647.888 ounces at 99.9% confidence level. Therefore, the predicted gold production for the year 2022 is 3.7million ounces at 99.9% confidence level.展开更多
Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturall...Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturally follows. It is even more appropriate to have a model(s) with few predictor variables. This paper seeks to identify appropriate statistical distribution functions for fitting gold production in Ghana. The empirical paper relied mainly on quarterly secondary datasets on gold production between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Weibull, Log-Normal, Generalized Extreme Value (GEV) were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC, AICc and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the reduced modified 3-parameter Weibull distribution provided the best fit for gold production in Ghana. Though the reduced modified Weibull function is proposed, it is important however to recognize that other external factors can influence production levels. Also, the average quarterly fitted gold production is 1000334.8918 ± 75,327.080 (±7.5%) [i.e., 925,007.812 – 1,075,661.972]. This indicates that the average annually fitted gold production lies between 3700031.248 and 4302647.888 ounces at 99.9% confidence level. Therefore, the predicted gold production for the year 2022 is 3.7million ounces at 99.9% confidence level.展开更多
Time series analysis has two goals, modeling random mechanisms and predicting future series using historical data. In the present work, a uni-variate time series autoregressive integrated moving average （ARIMA） mode...Time series analysis has two goals, modeling random mechanisms and predicting future series using historical data. In the present work, a uni-variate time series autoregressive integrated moving average （ARIMA） model has been developed for （a） simulating and forecasting mean rainfall, obtained using Theissen weights; over the Mahanadi River Basin in India, and （b） simula^ag and forecasting mean rainfall at 38 rain-gauge stations in district towns across the basin. For the analysis, monthly rainfall data of each district town for the years 1901-2002 （102 years） were used. Theissen weights were obtained over the basin and mean monthly rainfall was estimated. The trend and seasonality observed in ACF and PACF plots of rainfall data were removed using power transformation （a=0.5） and first order seasonal differencing prior to the development of the ARIMA model. Interestingly, the AR1MA model （1,0,0）（0,1,1）12 developed here was found to be most suitable for simulating and forecasting mean rainfall over the Mahanadi River Basin and for all 38 district town rain-gauge stations, separately. The Akaike Information Criterion （AIC）, good- ness of fit （Chi-square）, R2 （coefficient of determination）, MSE （mean square error） and MAE （mea absolute error） were used to test the validity and applicability of the developed ARIMA model at different stages. This model is considered appropriate to forecast the monthly rainfall for the upcoming 12 years in each district town to assist decision makers and policy makers establish priorities for water demand, storage, distribution, and disaster management.展开更多
The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lo...The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions,respectively.The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions,including the bivariate logistic Gumbel distribution,the bivariate lognormal distribution,and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously.We use the fully nested copulas to construct multivariate distributions taking into account related variables.Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater.We show that a bivariate model constructed by Frank copula gives the best reliability analysis,using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater,respectively.The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods.As copulas are suitable for constructing a bivariate or multivariate joint distribution,they have great potential in reliability analysis for other coastal structures.展开更多
We proposed </span><span style="font-family:Verdana;">“</span><span style="font-family:Verdana;">a new extension of three</span><span style="font-family:Verda...We proposed </span><span style="font-family:Verdana;">“</span><span style="font-family:Verdana;">a new extension of three</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">parametric distribution” called the inverse power two-parameter weighted Lindley (IPWL) distribution capable of modeling a upside-down bathtub hazard rate function. This distribution is studied to get basic structural properties such as reliability measures, moments, inverse moments and its related measures. Simulation studies </span><span style="font-family:Verdana;">are </span><span style="font-family:Verdana;">done to present the performance and behavior of maximum likelihood estimates of the IPWL distribution parameters. Finally, we perform goodness of fit measures and test statistics using a real data set to show the performance of the new distribution.展开更多
In this paper,a joint analysis consisting of goodness-of-fit tests and Markov chain Monte Carlo simulations are used to assess the performance of some ranked set sampling designs.The Markov chain Monte Carlo simulatio...In this paper,a joint analysis consisting of goodness-of-fit tests and Markov chain Monte Carlo simulations are used to assess the performance of some ranked set sampling designs.The Markov chain Monte Carlo simulations are conducted when Bayesian methods with Jeffery’s priors of the unknown parameters of Weibull distribution are used,while the goodness of fit analysis is conducted when the likelihood estimators are used and the corresponding empirical distributions are obtained.The ranked set sampling designs considered in this research are the usual ranked set sampling,extreme ranked set sampling,median ranked set sampling,and neoteric ranked set sampling designs.An intensive Monte Carlo simulation study is conducted using Lindley’s approximation algorithm to compute the different designs’-based estimators.The study showed that the dependent design“neoteric ranked set sampling design”is superior to other ranked set designs and the total relative efficiency is higher than the other designs’total relative efficiency.展开更多
Probable maximum precipitation(PMP) is widely used by hydrologists for appraisal of probable maximum flood(PMF)used for soil and water conservation structures, and design of dam spillways. A number of methods such as ...Probable maximum precipitation(PMP) is widely used by hydrologists for appraisal of probable maximum flood(PMF)used for soil and water conservation structures, and design of dam spillways. A number of methods such as empirical, statistical and dynamic are used to estimate PMP, the most favored being statistical and hydro-meteorological. In this paper,PMP estimation in mountainous regions of Pakistan is studied using statistical as well as physically based hydro-meteorological approaches. Daily precipitation, dew point, wind speed and temperature data is processed to estimate PMP for a one-day duration. Maximum precipitation for different return periods is estimated by using statistical approaches such as Gumble and Log-Pearson type-III(LP-III) distribution. Goodness of fit(GOF) test, chi-square test, correlation coefficient and coefficient of determination were applied to Gumble and LP-III distributions. Results reveal that among statistical approaches, Gumble distribution performed the best result compared to LP-III distribution. Isohyetal maps of the study area at different return periods are produced by using the GIS tool, and PMP in mountainous regions varies from 150 to 320 mm at an average value of 230.83 mm. The ratio of PMP for one-day duration to highest observed rainfall(HOR) varied from 1.08 to 1.29 with an average value of 1.18. An appropriate frequency factor(K_m) is very important which is a function of mean for observed precipitation and PMP for 1-day duration, and K_m values varies from 2.54 to 4.68. The coefficient of variability(C_v) varies from minimum value of 28% to maximum value of 43.35%. It was concluded that the statistical approach gives higher results compared to moisture maximization(MM) approach. In the hydro-meteorological approach, moisture maximization(MM) and wind moisture maximization(WMM) techniques were applied and it was concluded that wind moisture maximization approach gives higher results of PMP as compared to moisture maximization approach as well as for Hershfield technique. Therefore, it is suggested that MM approach is the most favored in the study area for PMP estimation, which leads to acceptable results, compared to WMM and statistical approaches.展开更多
In this paper,we suggested and studied the inverse length biased Maxell distribution(ILBMD)as a new continuous distribution of one parameter.The ILBMD is obtained by considering the inverse transformation technique of...In this paper,we suggested and studied the inverse length biased Maxell distribution(ILBMD)as a new continuous distribution of one parameter.The ILBMD is obtained by considering the inverse transformation technique of the Maxwell length biased distribution.Statistical characteristics of the ILBMD such as the moments,moment generating function,mode,quantile function,the coefficient of variation,coefficient of skewness,Moors and Bowley measures of kurtosis and skewness,stochastic ordering,stress-strength reliability,and mean deviations are obtained.In addition,the Bonferroni and Lorenz curves,Gini index,the reliability function,the hazard rate function,the reverse hazard rate function,the odds function,and the distributions of order statistics for the ILBMD,are presented.The ILBMD parameter is estimated using the maximum likelihood method,the method of moments,the maximum product of spacing technique,the ordinary and weight least square procedures,and the Cramer-Von-Mises methods.The Fishers information,as well as the Rényi and q-entropies,are derived.To investigate the usefulness of the proposed lifetime distribution and to illustrate the purpose of the study,a real dataset of the relief times of 20 patients receiving an analgesic is used.展开更多
Anderson-Darling （AD） sensing, characteristic function （CF） sensing and order statistic （OS） sensing are three common spectrum sensing （SS） methods based on goodness of fit （GOF） testing. However, AD and OS ...Anderson-Darling （AD） sensing, characteristic function （CF） sensing and order statistic （OS） sensing are three common spectrum sensing （SS） methods based on goodness of fit （GOF） testing. However, AD and OS sensing needs the prior information of noise variance; CF and OS sensing have high computation complexity. To circumvent those difficulties, in this paper, the ratio of the mean square to variance （RM2V） of the samples, after deriving its probability density function （PDF）, is employed as a test statistic to detect the availability of the vacant spectrum in the cognitive radio （CR） system. Then a blind SS method based on RM2V is proposed, which is dubbed as RM2V sensing, and its exact theoretical threshold is obtained via the derived PDF of RM2V. The performance of RM2V sensing is evaluated by theoretical analysis and Monte Carlo simulations. Comparing with the conventional energy detection （ED）, AD, CF and OS sensing, RM2V sensing, with no need of noise variance, has advantages from the aspect of computation complexity and detection performance.展开更多
In this paper,the properties and goodness of fit of exponential ratio type estimatorproposedbyKhanetal.(SciInt(Lahore)26(5):1897–1902,2014)havebeen carried out through simulation.It has been shown that estimator is c...In this paper,the properties and goodness of fit of exponential ratio type estimatorproposedbyKhanetal.(SciInt(Lahore)26(5):1897–1902,2014)havebeen carried out through simulation.It has been shown that estimator is consistent;the con-vergence of mean and variance of the estimator are discussed.The properties of some existing estimators based on simulation study have also been discussed.Goodness of fit test on the estimator has been carried out using Kolmogorov–Smirnov,Anderson–Darling,Cramer–von MisesandChi-squarestatistics.Fewstandarddistributionssuch as normal,Student t,Weibull and Cauchy distributions are fitted on the estimator.The best-fitted distribution on the estimator turned out to be normal distribution.展开更多
The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of c...The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.展开更多
基金This work was supported in part by the National Natural Science Foundation of China(No.61901408)in part by Natural Science Foundation of Jiangsu Province(No.BK20170512)in part by Universities Natural Science Research Project of Jiangsu Province(No.17KJB413003).
文摘In cognitive radio networks,spectrum sensing under circumstances of dynamically varying noise and lacking prior information is a key challenge to the conventional spectrum sensing algorithms.Since the necessary information is rather difficult to obtain practically,most existing spectrum sensing methods are fettered in applications.Motivated by these,in this paper,a Frequency domain Goodness of Fit Test(FGoF)based spectrum sensing method is proposed.The FGoF makes full use of underlying information in Guard-Bands and the advantages of GoF test works for any distribution.Analytical and simulated results show that the FGoF is a robust spectrum sensing method in cognitive radio with the inherent advantages of invulnerability to dynamically varying noise.
文摘The error distribution testing plays an important role in linear regression as distribution misspecification seriously affects the validity and efficiency of regression analysis. The least squares (OLS) residuals are often used to construct test statistics;in order to overcome the non-independent and identically residuals, the best linear unbiased scale (BLUS) residuals are applied in this paper, which, unlike OLS residuals, the residuals vector is identically and independently distributed. Based on the BLUS residuals, a new test statistic is constructed by using the sample random distance between sample quantile and quasi sample quantile derived from the null distribution, and the goodness-of-fit test of error distribution in the linear model is studied. The powers of the new tests under certain alternatives are examined. They are more powerful tests for the hypotheses concerned.
文摘A new six-parameter continuous distribution called the Generalized Kumaraswamy Generalized Power Gompertz (GKGPG) distribution is proposed in this study, a graphical illustration of the probability density function and cumulative distribution function is presented. The statistical features of the Generalized Kumaraswamy Generalized Power Gompertz distribution are systematically derived and adequately studied. The estimation of the model parameters in the absence of censoring and under-right censoring is performed using the method of maximum likelihood. The test statistic for right-censored data, criteria test for GKGPG distribution, estimated matrix Ŵ, Ĉ, and Ĝ, criteria test Y<sup>2</sup>n</sub>, alongside the quadratic form of the test statistic is derived. Mean simulated values of maximum likelihood estimates and their corresponding square mean errors are presented and confirmed to agree closely with the true parameter values. Simulated levels of significance for Y<sup>2</sup>n</sub> (γ) test for the GKGPG model against their theoretical values were recorded. We conclude that the null hypothesis for which simulated samples are fitted by GKGPG distribution is widely validated for the different levels of significance considered. From the summary of the results of the strength of a specific type of braided cord dataset on the GKGPG model, it is observed that the proposed GKGPG model fits the data set for a significance level ε = 0.05.
文摘Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.
文摘Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.
基金supported by the 10th Five-Year Plan Key Project of China and the National Science Foundation of China(grant No.40076028).
文摘Hydrologic frequency analysis plays an important role in coastal and ocean engineering for structural design and disaster prevention in coastal areas. This paper proposes a Nonlinear Least Squares Method (NLSM), which estimates the three unknown parameters of the Weibull distribution simultaneously by an iteration method. Statistical test shows that the NLSM fits each data sample well. The effects of different parameter-fitting methods, distribution models, and threshold values are also discussed in the statistical analysis of storm set-down elevation. The best-fitting probability distribution is given and the corresponding return values are estimated for engineering design.
文摘Confidence bands in a Normal Q-Q Plot allow us to detect non-normality of a data set rigorously, and in such a way that the conclusion does not depend on the subjectivity of the observer of the graph. In the construction of the graph, it is usual to fit a straight line to the plotted points, which serves both to check the hypothesis of normality (linear configuration of the plotted points) and to produce estimates of the parameters of the distribution. We can opt for dif-ferent types of lines. In this paper, we study the influence of five types of fitted straight lines in a Normal Q-Q Plot used for construction the confidence bands based on the exact distribution of the order statistics.
文摘Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturally follows. It is even more appropriate to have a model(s) with few predictor variables. This paper seeks to identify appropriate statistical distribution functions for fitting gold production in Ghana. The empirical paper relied mainly on quarterly secondary datasets on gold production between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Weibull, Log-Normal, Generalized Extreme Value (GEV) were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC, AICc and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the reduced modified 3-parameter Weibull distribution provided the best fit for gold production in Ghana. Though the reduced modified Weibull function is proposed, it is important however to recognize that other external factors can influence production levels. Also, the average quarterly fitted gold production is 1000334.8918 ± 75,327.080 (±7.5%) [i.e., 925,007.812 – 1,075,661.972]. This indicates that the average annually fitted gold production lies between 3700031.248 and 4302647.888 ounces at 99.9% confidence level. Therefore, the predicted gold production for the year 2022 is 3.7million ounces at 99.9% confidence level.
文摘Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturally follows. It is even more appropriate to have a model(s) with few predictor variables. This paper seeks to identify appropriate statistical distribution functions for fitting gold production in Ghana. The empirical paper relied mainly on quarterly secondary datasets on gold production between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Weibull, Log-Normal, Generalized Extreme Value (GEV) were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC, AICc and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the reduced modified 3-parameter Weibull distribution provided the best fit for gold production in Ghana. Though the reduced modified Weibull function is proposed, it is important however to recognize that other external factors can influence production levels. Also, the average quarterly fitted gold production is 1000334.8918 ± 75,327.080 (±7.5%) [i.e., 925,007.812 – 1,075,661.972]. This indicates that the average annually fitted gold production lies between 3700031.248 and 4302647.888 ounces at 99.9% confidence level. Therefore, the predicted gold production for the year 2022 is 3.7million ounces at 99.9% confidence level.
文摘Time series analysis has two goals, modeling random mechanisms and predicting future series using historical data. In the present work, a uni-variate time series autoregressive integrated moving average （ARIMA） model has been developed for （a） simulating and forecasting mean rainfall, obtained using Theissen weights; over the Mahanadi River Basin in India, and （b） simula^ag and forecasting mean rainfall at 38 rain-gauge stations in district towns across the basin. For the analysis, monthly rainfall data of each district town for the years 1901-2002 （102 years） were used. Theissen weights were obtained over the basin and mean monthly rainfall was estimated. The trend and seasonality observed in ACF and PACF plots of rainfall data were removed using power transformation （a=0.5） and first order seasonal differencing prior to the development of the ARIMA model. Interestingly, the AR1MA model （1,0,0）（0,1,1）12 developed here was found to be most suitable for simulating and forecasting mean rainfall over the Mahanadi River Basin and for all 38 district town rain-gauge stations, separately. The Akaike Information Criterion （AIC）, good- ness of fit （Chi-square）, R2 （coefficient of determination）, MSE （mean square error） and MAE （mea absolute error） were used to test the validity and applicability of the developed ARIMA model at different stages. This model is considered appropriate to forecast the monthly rainfall for the upcoming 12 years in each district town to assist decision makers and policy makers establish priorities for water demand, storage, distribution, and disaster management.
基金supported by the National Natural Science Foundation of China (51279186,51479183)the 111 Project (B14028)The first author thanks the Chinese Scholarship Council for funding his research in University of Washington
文摘The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions,respectively.The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions,including the bivariate logistic Gumbel distribution,the bivariate lognormal distribution,and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously.We use the fully nested copulas to construct multivariate distributions taking into account related variables.Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater.We show that a bivariate model constructed by Frank copula gives the best reliability analysis,using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater,respectively.The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods.As copulas are suitable for constructing a bivariate or multivariate joint distribution,they have great potential in reliability analysis for other coastal structures.
文摘We proposed </span><span style="font-family:Verdana;">“</span><span style="font-family:Verdana;">a new extension of three</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">parametric distribution” called the inverse power two-parameter weighted Lindley (IPWL) distribution capable of modeling a upside-down bathtub hazard rate function. This distribution is studied to get basic structural properties such as reliability measures, moments, inverse moments and its related measures. Simulation studies </span><span style="font-family:Verdana;">are </span><span style="font-family:Verdana;">done to present the performance and behavior of maximum likelihood estimates of the IPWL distribution parameters. Finally, we perform goodness of fit measures and test statistics using a real data set to show the performance of the new distribution.
文摘In this paper,a joint analysis consisting of goodness-of-fit tests and Markov chain Monte Carlo simulations are used to assess the performance of some ranked set sampling designs.The Markov chain Monte Carlo simulations are conducted when Bayesian methods with Jeffery’s priors of the unknown parameters of Weibull distribution are used,while the goodness of fit analysis is conducted when the likelihood estimators are used and the corresponding empirical distributions are obtained.The ranked set sampling designs considered in this research are the usual ranked set sampling,extreme ranked set sampling,median ranked set sampling,and neoteric ranked set sampling designs.An intensive Monte Carlo simulation study is conducted using Lindley’s approximation algorithm to compute the different designs’-based estimators.The study showed that the dependent design“neoteric ranked set sampling design”is superior to other ranked set designs and the total relative efficiency is higher than the other designs’total relative efficiency.
基金supported by Centre of Excellence in Water Resources Engineering,University of Engineering and Technology Lahore
文摘Probable maximum precipitation(PMP) is widely used by hydrologists for appraisal of probable maximum flood(PMF)used for soil and water conservation structures, and design of dam spillways. A number of methods such as empirical, statistical and dynamic are used to estimate PMP, the most favored being statistical and hydro-meteorological. In this paper,PMP estimation in mountainous regions of Pakistan is studied using statistical as well as physically based hydro-meteorological approaches. Daily precipitation, dew point, wind speed and temperature data is processed to estimate PMP for a one-day duration. Maximum precipitation for different return periods is estimated by using statistical approaches such as Gumble and Log-Pearson type-III(LP-III) distribution. Goodness of fit(GOF) test, chi-square test, correlation coefficient and coefficient of determination were applied to Gumble and LP-III distributions. Results reveal that among statistical approaches, Gumble distribution performed the best result compared to LP-III distribution. Isohyetal maps of the study area at different return periods are produced by using the GIS tool, and PMP in mountainous regions varies from 150 to 320 mm at an average value of 230.83 mm. The ratio of PMP for one-day duration to highest observed rainfall(HOR) varied from 1.08 to 1.29 with an average value of 1.18. An appropriate frequency factor(K_m) is very important which is a function of mean for observed precipitation and PMP for 1-day duration, and K_m values varies from 2.54 to 4.68. The coefficient of variability(C_v) varies from minimum value of 28% to maximum value of 43.35%. It was concluded that the statistical approach gives higher results compared to moisture maximization(MM) approach. In the hydro-meteorological approach, moisture maximization(MM) and wind moisture maximization(WMM) techniques were applied and it was concluded that wind moisture maximization approach gives higher results of PMP as compared to moisture maximization approach as well as for Hershfield technique. Therefore, it is suggested that MM approach is the most favored in the study area for PMP estimation, which leads to acceptable results, compared to WMM and statistical approaches.
基金A.R.A.Alanzi would like to thank the Deanship of Scientific Research at Majmaah University for financial support and encouragement.
文摘In this paper,we suggested and studied the inverse length biased Maxell distribution(ILBMD)as a new continuous distribution of one parameter.The ILBMD is obtained by considering the inverse transformation technique of the Maxwell length biased distribution.Statistical characteristics of the ILBMD such as the moments,moment generating function,mode,quantile function,the coefficient of variation,coefficient of skewness,Moors and Bowley measures of kurtosis and skewness,stochastic ordering,stress-strength reliability,and mean deviations are obtained.In addition,the Bonferroni and Lorenz curves,Gini index,the reliability function,the hazard rate function,the reverse hazard rate function,the odds function,and the distributions of order statistics for the ILBMD,are presented.The ILBMD parameter is estimated using the maximum likelihood method,the method of moments,the maximum product of spacing technique,the ordinary and weight least square procedures,and the Cramer-Von-Mises methods.The Fishers information,as well as the Rényi and q-entropies,are derived.To investigate the usefulness of the proposed lifetime distribution and to illustrate the purpose of the study,a real dataset of the relief times of 20 patients receiving an analgesic is used.
基金supported by Natural Science Foundation of China(6127127661301091)Natural Science Foundation of Shaanxi Province(2014JM8299)
文摘Anderson-Darling （AD） sensing, characteristic function （CF） sensing and order statistic （OS） sensing are three common spectrum sensing （SS） methods based on goodness of fit （GOF） testing. However, AD and OS sensing needs the prior information of noise variance; CF and OS sensing have high computation complexity. To circumvent those difficulties, in this paper, the ratio of the mean square to variance （RM2V） of the samples, after deriving its probability density function （PDF）, is employed as a test statistic to detect the availability of the vacant spectrum in the cognitive radio （CR） system. Then a blind SS method based on RM2V is proposed, which is dubbed as RM2V sensing, and its exact theoretical threshold is obtained via the derived PDF of RM2V. The performance of RM2V sensing is evaluated by theoretical analysis and Monte Carlo simulations. Comparing with the conventional energy detection （ED）, AD, CF and OS sensing, RM2V sensing, with no need of noise variance, has advantages from the aspect of computation complexity and detection performance.
文摘In this paper,the properties and goodness of fit of exponential ratio type estimatorproposedbyKhanetal.(SciInt(Lahore)26(5):1897–1902,2014)havebeen carried out through simulation.It has been shown that estimator is consistent;the con-vergence of mean and variance of the estimator are discussed.The properties of some existing estimators based on simulation study have also been discussed.Goodness of fit test on the estimator has been carried out using Kolmogorov–Smirnov,Anderson–Darling,Cramer–von MisesandChi-squarestatistics.Fewstandarddistributionssuch as normal,Student t,Weibull and Cauchy distributions are fitted on the estimator.The best-fitted distribution on the estimator turned out to be normal distribution.
基金supported by the Natural Science Foundation of China under Grant Nos.11071022,11028103,11231010,11471223,BCMIISthe Beijing Municipal Educational Commission Foundation under Grant Nos.KZ201410028030,KM201210028005Jishou University Subject in 2014(No:14JD035)
文摘The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.
