In this paper,we propose a new extension of the traditional Rayleigh distribution called the modified Kies Rayleigh distribution.The new distribution contains one scale and one shape parameter and its hazard rate func...In this paper,we propose a new extension of the traditional Rayleigh distribution called the modified Kies Rayleigh distribution.The new distribution contains one scale and one shape parameter and its hazard rate function can be increasing and bathtub-shaped.Some mathematical properties of the new distribution are derived including quantiles and moments.The parameters of modified Kies Rayleigh distribution are estimated based on progressively Type-II censored data.For this purpose,we consider two estimation methods,namely maximum likelihood and maximum product of spacing estimation methods.To compare the efficiency of the proposed estimators,a simulation study is carried out.To show the applicability of the new model as well as the estimation methods,one real data for failure times of software is analyzed.Based on the empirical parts,we can conclude that the proposed model can be considered as a good model in the field of life testing and reliability analysis compared with other competing models.展开更多
We study in this manuscript a new one-parameter model called sine inverse Rayleigh(SIR)model that is a new extension of the classical inverse Rayleigh model.The sine inverse Rayleigh model is aiming to provide morefit-...We study in this manuscript a new one-parameter model called sine inverse Rayleigh(SIR)model that is a new extension of the classical inverse Rayleigh model.The sine inverse Rayleigh model is aiming to provide morefit-ting for real data sets of purposes.The proposed extension is moreflexible than the original inverse Rayleigh(IR)model and it hasmany applications in physics and medicine.The sine inverse Rayleigh distribution can havea uni-model and right skewed probability density function(PDF).The hazard rate function(HRF)of sine inverse Rayleigh distribution can be increasing and J-shaped.Sev-eral of thenew model’s fundamental characteristics,namely quantile function,moments,incompletemoments,Lorenz and Bonferroni Curves are studied.Four classical estimation methods forthe population parameters,namely least squares(LS),weighted least squares(WLS),maximum likelihood(ML),and percentile(PC)methods are discussed,and the performanceof the four estimators(namely LS,WLS,ML and PC estimators)are also compared bynumerical implementa-tions.Finally,three sets of real data are utilized to compare the behavior of the four employed methods forfinding an optimal estimation of the new distribution.展开更多
<span style="font-family:Verdana;">In this paper, we derived a new distribution named as truncated Weibull Rayleigh (TW-R) distribution. Its characterization and statistical properties are obtained, su...<span style="font-family:Verdana;">In this paper, we derived a new distribution named as truncated Weibull Rayleigh (TW-R) distribution. Its characterization and statistical properties are obtained, such as reliability function, hazard function, reversed</span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">hazard rate function, cumulative hazard rate function, quantile function, rth moment, incomplete moments, Rényi and q entropies and order statistic. Parameter estimation is implemented using method of maximum-likelihood estimation and Fisher information matrix is derived. Finally, application of the presented new distribution to a real data representing the failure times of 63 airbcraft</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Windshield is given and its goodness-of-fit is demonstrated. In addition to, comparisons to other models are implemented to show the flexibility of the presented</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">model.</span></span></span>展开更多
Lifetime performance index is a powerful and effective way to analyze whether a product achieves the specified standards.In this paper,we investigate the lifetime performance index for the inverted exponential Rayleig...Lifetime performance index is a powerful and effective way to analyze whether a product achieves the specified standards.In this paper,we investigate the lifetime performance index for the inverted exponential Rayleigh distribution using progressive type II censored sample data.The censored sample is able to greatly save the cost of the experiment and speed up the experiment.We derive the estimation value of lifetime performance index using the maximum likelihood method,and conduct the hypothesis test.Based on extensive numerical simulation,the power function is utilized to assess effectiveness of hypothesis testing.The simulation results show that lifetime performance index is good for determining whether the lifetime of the product reaches the criterion.Finally,a practical dataset is provided to give a demonstration for the procedures of lifetime performance evaluation.展开更多
This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units re...This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.展开更多
In the present study, wind speed data of Jumla, Nepal have been statistically analyzed. For this purpose, the daily averaged wind speed data for 10 year period (2004-2014: 2012 excluded) provided by Department of Hydr...In the present study, wind speed data of Jumla, Nepal have been statistically analyzed. For this purpose, the daily averaged wind speed data for 10 year period (2004-2014: 2012 excluded) provided by Department of Hydrology and Meteorology (DHM) was analyzed to estimate wind power density. Wind speed as high as 18 m/s was recorded at height of 10 m. Annual mean wind speed was ascertained to be decreasing from 7.35 m/s in 2004 to 5.13 m/s in 2014 as a consequence of Global Climate Change. This is a subject of concern looking at government’s plan to harness wind energy. Monthly wind speed plot shows that the fastest wind speed is generally in month of June (Monsoon Season) and slowest in December/January (Winter Season). Results presented Weibull distribution to fit measured probability distribution better than the Rayleigh distribution for whole years in High altitude region of Nepal. Average value of wind power density based on mean and root mean cube seed approaches were 131.31 W/m<sup>2</sup>/year and 184.93 W/m<sup>2</sup>/year respectively indicating that Jumla stands in class III. Weibull distribution shows a good approximation for estimation of power density with maximum error of 3.68% when root mean cube speed is taken as reference.展开更多
Energy is an essential element for any civilized country’s social and economic development,but the use of fossil fuels and nonrenewable energy forms has many negative impacts on the environment and the ecosystem.The ...Energy is an essential element for any civilized country’s social and economic development,but the use of fossil fuels and nonrenewable energy forms has many negative impacts on the environment and the ecosystem.The Republic of Yemen has very good potential to use renewable energy.Unfortunately,we find few studies on renewable wind energy in Yemen.Given the lack of a similar analysis for the coastal city,this research newly investigates wind energy’s potential near the Almukalla area by analyzing wind characteristics.Thus,evaluation,model identification,determination of available energy density,computing the capacity factors for several wind turbines and calculation of wind energy were extracted at three heights of 15,30,and 50meters.Average wind speeds were obtained only for the currently available data of five recent years,2005–2009.This study involves a preliminary assessment of Almukalla’s wind energy potential to provide a primary base and useful insights for wind engineers and experts.This research aims to provide useful assessment of the potential of wind energy in Almukalla for developing wind energy and an efficient wind approach.The Weibull distribution shows a perfect approximation for estimating the intensity of Yemen’s wind energy.Depending on both theWeibullmodel and the results of the annual wind speed data analysis for the study site in Mukalla,the capacity factor for many turbines was also calculated,and the best suitable turbine was selected.According to the International Wind Energy Rating criteria,Almukalla falls under Category 7,which is,rated“Superb”most of the year.展开更多
This paper puts forward a new method of realtime reconstruction of fluid in natural scene.It takes the measure of combination of image analysis and LBM(Lattice Boltz-mann Methods).First,employs LK(Lucas–Kanade)method...This paper puts forward a new method of realtime reconstruction of fluid in natural scene.It takes the measure of combination of image analysis and LBM(Lattice Boltz-mann Methods).First,employs LK(Lucas–Kanade)method to calculate the dense optical flow,and then takes LBM to obtain the joint force of central particles for the initial result.After backfilling the velocity vectors field,it adopts the K-means cluster to obtain several classes,in each class,it takes advantage of the Rayleigh distribution to fit the height field of fluid.Finally,the reconstruction result of fluid is obtained.In addition,it demonstrates the results of the height field of fluid in the experiment.Fur-ther experiments shows that it is a valid method of fluid reconstruction with real time and can be used in the study of natural landscape fluid with efficiency and feasibility.展开更多
基金the Deanship Scientific Research(DSR)King Abdulaziz University,Jeddah under Grant No.(G:337-130-1441).
文摘In this paper,we propose a new extension of the traditional Rayleigh distribution called the modified Kies Rayleigh distribution.The new distribution contains one scale and one shape parameter and its hazard rate function can be increasing and bathtub-shaped.Some mathematical properties of the new distribution are derived including quantiles and moments.The parameters of modified Kies Rayleigh distribution are estimated based on progressively Type-II censored data.For this purpose,we consider two estimation methods,namely maximum likelihood and maximum product of spacing estimation methods.To compare the efficiency of the proposed estimators,a simulation study is carried out.To show the applicability of the new model as well as the estimation methods,one real data for failure times of software is analyzed.Based on the empirical parts,we can conclude that the proposed model can be considered as a good model in the field of life testing and reliability analysis compared with other competing models.
文摘We study in this manuscript a new one-parameter model called sine inverse Rayleigh(SIR)model that is a new extension of the classical inverse Rayleigh model.The sine inverse Rayleigh model is aiming to provide morefit-ting for real data sets of purposes.The proposed extension is moreflexible than the original inverse Rayleigh(IR)model and it hasmany applications in physics and medicine.The sine inverse Rayleigh distribution can havea uni-model and right skewed probability density function(PDF).The hazard rate function(HRF)of sine inverse Rayleigh distribution can be increasing and J-shaped.Sev-eral of thenew model’s fundamental characteristics,namely quantile function,moments,incompletemoments,Lorenz and Bonferroni Curves are studied.Four classical estimation methods forthe population parameters,namely least squares(LS),weighted least squares(WLS),maximum likelihood(ML),and percentile(PC)methods are discussed,and the performanceof the four estimators(namely LS,WLS,ML and PC estimators)are also compared bynumerical implementa-tions.Finally,three sets of real data are utilized to compare the behavior of the four employed methods forfinding an optimal estimation of the new distribution.
文摘<span style="font-family:Verdana;">In this paper, we derived a new distribution named as truncated Weibull Rayleigh (TW-R) distribution. Its characterization and statistical properties are obtained, such as reliability function, hazard function, reversed</span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">hazard rate function, cumulative hazard rate function, quantile function, rth moment, incomplete moments, Rényi and q entropies and order statistic. Parameter estimation is implemented using method of maximum-likelihood estimation and Fisher information matrix is derived. Finally, application of the presented new distribution to a real data representing the failure times of 63 airbcraft</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Windshield is given and its goodness-of-fit is demonstrated. In addition to, comparisons to other models are implemented to show the flexibility of the presented</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">model.</span></span></span>
文摘Lifetime performance index is a powerful and effective way to analyze whether a product achieves the specified standards.In this paper,we investigate the lifetime performance index for the inverted exponential Rayleigh distribution using progressive type II censored sample data.The censored sample is able to greatly save the cost of the experiment and speed up the experiment.We derive the estimation value of lifetime performance index using the maximum likelihood method,and conduct the hypothesis test.Based on extensive numerical simulation,the power function is utilized to assess effectiveness of hypothesis testing.The simulation results show that lifetime performance index is good for determining whether the lifetime of the product reaches the criterion.Finally,a practical dataset is provided to give a demonstration for the procedures of lifetime performance evaluation.
基金supported by the National Statistical Science Research Project of China(2019LZ32)
文摘This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.
文摘In the present study, wind speed data of Jumla, Nepal have been statistically analyzed. For this purpose, the daily averaged wind speed data for 10 year period (2004-2014: 2012 excluded) provided by Department of Hydrology and Meteorology (DHM) was analyzed to estimate wind power density. Wind speed as high as 18 m/s was recorded at height of 10 m. Annual mean wind speed was ascertained to be decreasing from 7.35 m/s in 2004 to 5.13 m/s in 2014 as a consequence of Global Climate Change. This is a subject of concern looking at government’s plan to harness wind energy. Monthly wind speed plot shows that the fastest wind speed is generally in month of June (Monsoon Season) and slowest in December/January (Winter Season). Results presented Weibull distribution to fit measured probability distribution better than the Rayleigh distribution for whole years in High altitude region of Nepal. Average value of wind power density based on mean and root mean cube seed approaches were 131.31 W/m<sup>2</sup>/year and 184.93 W/m<sup>2</sup>/year respectively indicating that Jumla stands in class III. Weibull distribution shows a good approximation for estimation of power density with maximum error of 3.68% when root mean cube speed is taken as reference.
文摘Energy is an essential element for any civilized country’s social and economic development,but the use of fossil fuels and nonrenewable energy forms has many negative impacts on the environment and the ecosystem.The Republic of Yemen has very good potential to use renewable energy.Unfortunately,we find few studies on renewable wind energy in Yemen.Given the lack of a similar analysis for the coastal city,this research newly investigates wind energy’s potential near the Almukalla area by analyzing wind characteristics.Thus,evaluation,model identification,determination of available energy density,computing the capacity factors for several wind turbines and calculation of wind energy were extracted at three heights of 15,30,and 50meters.Average wind speeds were obtained only for the currently available data of five recent years,2005–2009.This study involves a preliminary assessment of Almukalla’s wind energy potential to provide a primary base and useful insights for wind engineers and experts.This research aims to provide useful assessment of the potential of wind energy in Almukalla for developing wind energy and an efficient wind approach.The Weibull distribution shows a perfect approximation for estimating the intensity of Yemen’s wind energy.Depending on both theWeibullmodel and the results of the annual wind speed data analysis for the study site in Mukalla,the capacity factor for many turbines was also calculated,and the best suitable turbine was selected.According to the International Wind Energy Rating criteria,Almukalla falls under Category 7,which is,rated“Superb”most of the year.
基金the Natural Science Foundation of Shanghai Science and Technology Commission in China(Grant 11ZR1411100)National Natural Science Foundation of China(F030120)for funding this project.
文摘This paper puts forward a new method of realtime reconstruction of fluid in natural scene.It takes the measure of combination of image analysis and LBM(Lattice Boltz-mann Methods).First,employs LK(Lucas–Kanade)method to calculate the dense optical flow,and then takes LBM to obtain the joint force of central particles for the initial result.After backfilling the velocity vectors field,it adopts the K-means cluster to obtain several classes,in each class,it takes advantage of the Rayleigh distribution to fit the height field of fluid.Finally,the reconstruction result of fluid is obtained.In addition,it demonstrates the results of the height field of fluid in the experiment.Fur-ther experiments shows that it is a valid method of fluid reconstruction with real time and can be used in the study of natural landscape fluid with efficiency and feasibility.
