In the present study, the surface elevation of wind waves observed in laboratory and in the Bohai Sea are adopted for the estimation of the wind wave frequency spectrtm by use of the method of the arcsine law （MAL）....In the present study, the surface elevation of wind waves observed in laboratory and in the Bohai Sea are adopted for the estimation of the wind wave frequency spectrtm by use of the method of the arcsine law （MAL）. The traditional method uses the surface elevation to calculate the correlation and then estimate the frequency spectrum while the MAL, presented by Yu and l.an （1979）, uses the time sequence of zero-crossing points of surface elevation rather than directly the surface elevation to calculate the correlation. 66 sets of wind wave data obtained in laboratory and 420 sets of data observed in the Bohai Sea are adopted for the examination of the method introduced by Yu and Lan. Results show that the MAL can give reliable estimation of wind wave spectra. Correlation and form of spectra estimated by the MAL are similar to those estimated by the traditional method. The peak frequency and the spectral density in peak frequency by the MAL are close to those obtained by the traditional method.展开更多
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
基金This project was financially supported by the National Natural Science Foundation of China(Grant No.40406008) the Foundation for Open Projects of the Key Laboratory of Physical Oceanography,Ministry of Education,China(Grant No.200309)
文摘In the present study, the surface elevation of wind waves observed in laboratory and in the Bohai Sea are adopted for the estimation of the wind wave frequency spectrtm by use of the method of the arcsine law （MAL）. The traditional method uses the surface elevation to calculate the correlation and then estimate the frequency spectrum while the MAL, presented by Yu and l.an （1979）, uses the time sequence of zero-crossing points of surface elevation rather than directly the surface elevation to calculate the correlation. 66 sets of wind wave data obtained in laboratory and 420 sets of data observed in the Bohai Sea are adopted for the examination of the method introduced by Yu and Lan. Results show that the MAL can give reliable estimation of wind wave spectra. Correlation and form of spectra estimated by the MAL are similar to those estimated by the traditional method. The peak frequency and the spectral density in peak frequency by the MAL are close to those obtained by the traditional method.
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.
