The heavy-tailed distributions are very useful and play a major role in actuary and financial management problems.Actuaries are often searching for such distributions to provide the best fit to financial and economic ...The heavy-tailed distributions are very useful and play a major role in actuary and financial management problems.Actuaries are often searching for such distributions to provide the best fit to financial and economic data sets.In the current study,a prominent method to generate new distributions useful for modeling heavy-tailed data is considered.The proposed family is introduced using trigonometric function and can be named as the Arcsine-X family of distri-butions.For the purposes of the demonstration,a specific sub-model of the proposed family,called the Arcsine-Weibull distribution is considered.The max-imum likelihood estimation method is adopted for estimating the parameters of the Arcsine-X distributions.The resultant estimators are evaluated in a detailed Monte Carlo simulation study.To illustrate the Arcsine-Weibull two insurance data sets are analyzed.Comparison of the Arcsine-Weibull model is done with the well-known two parameters and four parameters competitors.The competitive models including the Weibull,Lomax,Burr-XII and beta Weibull models.Different goodness of fit measures are taken into account to determine the useful-ness of the Arcsine-Weibull and other considered models.Data analysis shows that the Arcsine-Weibull distribution works much better than competing models in financial data analysis.展开更多
Background: When continuous scale measurements are available, agreements between two measuring devices are assessed both graphically and analytically. In clinical investigations, Bland and Altman proposed plotting sub...Background: When continuous scale measurements are available, agreements between two measuring devices are assessed both graphically and analytically. In clinical investigations, Bland and Altman proposed plotting subject-wise differences between raters against subject-wise averages. In order to scientifically assess agreement, Bartko recommended combining the graphical approach with the statistical analytic procedure suggested by Bradley and Blackwood. The advantage of using this approach is that it enables significance testing and sample size estimation. We noted that the direct use of the results of the regression is misleading and we provide a correction in this regard. Methods: Graphical and linear models are used to assess agreements for continuous scale measurements. We demonstrate that software linear regression results should not be readily used and we provided correct analytic procedures. The degrees of freedom of the F-statistics are incorrectly reported, and we propose methods to overcome this problem by introducing the correct analytic form of the F statistic. Methods for sample size estimation using R-functions are also given. Results: We believe that the tutorial and the R-codes are useful tools for testing and estimating agreement between two rating protocols for continuous scale measurements. The interested reader may use the codes and apply them to their available data when the issue of agreement between two raters is the subject of interest.展开更多
Recently attention has been drawn to the frequently observed fifth power of the golden mean in many disciplines of science and technology. Whereas in a forthcoming contribution the focus will be directed towards <i...Recently attention has been drawn to the frequently observed fifth power of the golden mean in many disciplines of science and technology. Whereas in a forthcoming contribution the focus will be directed towards <i>Fibonacci</i> number-based helical structures of living as well as inorganic matter, in this short letter the geometry of the Great Pyramid of the ancient Egyptians was investigated once more. The surprising main result is that the ratio of the in-sphere volume of the pyramid and the pyramid volume itself is given by π⋅<i>φ</i><sup>5</sup>, where <i>φ</i> = 0.618033987<span style="white-space:nowrap;">⋅<span style="white-space:nowrap;">⋅</span><span style="white-space:nowrap;">⋅</span></span> is nature’s most important number, the golden mean. In this way not only phase transitions from microscopic to cosmic scale are connected with <i>φ</i><sup>5</sup>, also ingenious ancient builders have intuitively guessed its magic before.展开更多
Since 2016,a number of studies have been published on standard decoctions used in Chinese medicine.However,there is little research on statistical issues related to establishing the quality standards for standard deco...Since 2016,a number of studies have been published on standard decoctions used in Chinese medicine.However,there is little research on statistical issues related to establishing the quality standards for standard decoctions.In view of the currently established quality standard methods for standard decoctions,an improvement scheme is proposed from a statistical perspective.This review explores the requirements for dry matter yield rate data and index component transfer data for the application of two methods specified in‘‘Technical Requirements for Quality Control and Standard Establishment of Chinese Medicine Formula Granules,"which include the average value plus or minus three times the standard deviation (■±3SD) or 70%to 130%of the average value (■±30%■).The square-root arcsine transformation method is used as an approach to solve the problem of unreasonable standard ranges of standard decoctions.This review also proposes the use of merged data to establish a standard.A method to judge whether multiple sets of standard decoction data can be merged is also provided.When multiple sets of data have a similar central tendency and a similar discrete tendency,they can be merged to establish a more reliable quality standard.Assuming that the dry matter yield rate and transfer rate conform to a binomial distribution,the number of batches of prepared slices that are needed to establish the standard decoction quality standard is estimated.It is recommended that no less than 30 batches of prepared slices should be used for the establishment of standard decoction quality standards.展开更多
文摘The heavy-tailed distributions are very useful and play a major role in actuary and financial management problems.Actuaries are often searching for such distributions to provide the best fit to financial and economic data sets.In the current study,a prominent method to generate new distributions useful for modeling heavy-tailed data is considered.The proposed family is introduced using trigonometric function and can be named as the Arcsine-X family of distri-butions.For the purposes of the demonstration,a specific sub-model of the proposed family,called the Arcsine-Weibull distribution is considered.The max-imum likelihood estimation method is adopted for estimating the parameters of the Arcsine-X distributions.The resultant estimators are evaluated in a detailed Monte Carlo simulation study.To illustrate the Arcsine-Weibull two insurance data sets are analyzed.Comparison of the Arcsine-Weibull model is done with the well-known two parameters and four parameters competitors.The competitive models including the Weibull,Lomax,Burr-XII and beta Weibull models.Different goodness of fit measures are taken into account to determine the useful-ness of the Arcsine-Weibull and other considered models.Data analysis shows that the Arcsine-Weibull distribution works much better than competing models in financial data analysis.
文摘Background: When continuous scale measurements are available, agreements between two measuring devices are assessed both graphically and analytically. In clinical investigations, Bland and Altman proposed plotting subject-wise differences between raters against subject-wise averages. In order to scientifically assess agreement, Bartko recommended combining the graphical approach with the statistical analytic procedure suggested by Bradley and Blackwood. The advantage of using this approach is that it enables significance testing and sample size estimation. We noted that the direct use of the results of the regression is misleading and we provide a correction in this regard. Methods: Graphical and linear models are used to assess agreements for continuous scale measurements. We demonstrate that software linear regression results should not be readily used and we provided correct analytic procedures. The degrees of freedom of the F-statistics are incorrectly reported, and we propose methods to overcome this problem by introducing the correct analytic form of the F statistic. Methods for sample size estimation using R-functions are also given. Results: We believe that the tutorial and the R-codes are useful tools for testing and estimating agreement between two rating protocols for continuous scale measurements. The interested reader may use the codes and apply them to their available data when the issue of agreement between two raters is the subject of interest.
文摘Recently attention has been drawn to the frequently observed fifth power of the golden mean in many disciplines of science and technology. Whereas in a forthcoming contribution the focus will be directed towards <i>Fibonacci</i> number-based helical structures of living as well as inorganic matter, in this short letter the geometry of the Great Pyramid of the ancient Egyptians was investigated once more. The surprising main result is that the ratio of the in-sphere volume of the pyramid and the pyramid volume itself is given by π⋅<i>φ</i><sup>5</sup>, where <i>φ</i> = 0.618033987<span style="white-space:nowrap;">⋅<span style="white-space:nowrap;">⋅</span><span style="white-space:nowrap;">⋅</span></span> is nature’s most important number, the golden mean. In this way not only phase transitions from microscopic to cosmic scale are connected with <i>φ</i><sup>5</sup>, also ingenious ancient builders have intuitively guessed its magic before.
基金supported by National S&T Major Project of China (2018ZX09201011-002)the Student Research Training Program of the College of Pharmaceutical Sciences of Zhejiang University (Y201936333)the National Project for Standardization of Chinese Materia Medica (ZYBZH-C-GD-04)
文摘Since 2016,a number of studies have been published on standard decoctions used in Chinese medicine.However,there is little research on statistical issues related to establishing the quality standards for standard decoctions.In view of the currently established quality standard methods for standard decoctions,an improvement scheme is proposed from a statistical perspective.This review explores the requirements for dry matter yield rate data and index component transfer data for the application of two methods specified in‘‘Technical Requirements for Quality Control and Standard Establishment of Chinese Medicine Formula Granules,"which include the average value plus or minus three times the standard deviation (■±3SD) or 70%to 130%of the average value (■±30%■).The square-root arcsine transformation method is used as an approach to solve the problem of unreasonable standard ranges of standard decoctions.This review also proposes the use of merged data to establish a standard.A method to judge whether multiple sets of standard decoction data can be merged is also provided.When multiple sets of data have a similar central tendency and a similar discrete tendency,they can be merged to establish a more reliable quality standard.Assuming that the dry matter yield rate and transfer rate conform to a binomial distribution,the number of batches of prepared slices that are needed to establish the standard decoction quality standard is estimated.It is recommended that no less than 30 batches of prepared slices should be used for the establishment of standard decoction quality standards.
