Mardia (1970) defined a measure of multivariate kurtosis and derived its asymptotic distributionfor samples from a multivariate normal population. Some new results on elliptical distributions areused to extend Mardia&...Mardia (1970) defined a measure of multivariate kurtosis and derived its asymptotic distributionfor samples from a multivariate normal population. Some new results on elliptical distributions areused to extend Mardia's results to samples from an elliptical distribution. These results provide amethod for testing hypotheses on the kurtosis parameter of elliptical distributions. An appendixprovides extensions of Kendall and Stuart's (1977) standard errors of bivariate moments to the thirdand fourth order.展开更多
In this paper,the Rama distribution(RD)is considered,and a new model called extended Rama distribution(ERD)is suggested.The new model involves the sum of two independent Rama distributed random variables.The probabili...In this paper,the Rama distribution(RD)is considered,and a new model called extended Rama distribution(ERD)is suggested.The new model involves the sum of two independent Rama distributed random variables.The probability density function(pdf)and cumulative distribution function(cdf)are obtained and analyzed.It is found that the new model is skewed to the right.Several mathematical and statistical properties are derived and proved.The properties studied include moments,coefficient of variation,coefficient of skewness,coefficient of kurtosis and moment generating function.Some simulations are undertaken to illustrate the behavior of these properties.In addition,the reliability analysis of the distribution is investigated through the hazard rate function,reversed hazard rate function and odds function.The parameter of the distribution is estimated based on the maximum likelihood method.The distributions of order statistics for ERD are also presented.The performance of the suggested model is compared with several other lifetime distributions based on some goodness of fit tests on a real dataset.It turns out that the suggested model is more flexible than its competitors considered in this study,for modeling real lifetime data.展开更多
基金This research was supported by grant DA01070 from the U. S Public Health Servies. Production assistance of Jnlie Speckart is gratefully acknowledged. Requests for reprints should be sent to: P. M. Bentler. Department of Psychology, University of Californ
文摘Mardia (1970) defined a measure of multivariate kurtosis and derived its asymptotic distributionfor samples from a multivariate normal population. Some new results on elliptical distributions areused to extend Mardia's results to samples from an elliptical distribution. These results provide amethod for testing hypotheses on the kurtosis parameter of elliptical distributions. An appendixprovides extensions of Kendall and Stuart's (1977) standard errors of bivariate moments to the thirdand fourth order.
基金The authors extend their appreciation to Universiti Kebangsaan Malaysia for providing a partial funding for the work under the grant number GGPM-2017-124 and TAP-K017073 which were obtained by Mohd Aftar Abu Bakar.
文摘In this paper,the Rama distribution(RD)is considered,and a new model called extended Rama distribution(ERD)is suggested.The new model involves the sum of two independent Rama distributed random variables.The probability density function(pdf)and cumulative distribution function(cdf)are obtained and analyzed.It is found that the new model is skewed to the right.Several mathematical and statistical properties are derived and proved.The properties studied include moments,coefficient of variation,coefficient of skewness,coefficient of kurtosis and moment generating function.Some simulations are undertaken to illustrate the behavior of these properties.In addition,the reliability analysis of the distribution is investigated through the hazard rate function,reversed hazard rate function and odds function.The parameter of the distribution is estimated based on the maximum likelihood method.The distributions of order statistics for ERD are also presented.The performance of the suggested model is compared with several other lifetime distributions based on some goodness of fit tests on a real dataset.It turns out that the suggested model is more flexible than its competitors considered in this study,for modeling real lifetime data.
