Asymptotic Distribution and Moments of Normal Extremes

Moments and Absolute Moments of the Normal Distribution

We present formulas for the (raw and central) moments and absolute moments of the normal distribution. We note that these results are not new, yet many textbooks miss out on at least some of them. Hence, we believe that it is worthwhile to collect these formulas and their derivations in these notes.

Asymptotic expansions for distributions of extremes from generalized Maxwell distribution

In this paper, with optimal normalized constants, the asymptotic expansions of the distribution of the normalized maxima from generalized Maxwell distribution is derived. It shows that the convergence rate of the normalized maxima to the Gumbel extreme value distribution is proportional to 1/ log n.

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Asymptotic Efficiencies of the MLE Based on Bivariate Record Values from Bivariate Normal Distribution

Abstract. Maximum likelihood (ML) estimation based on bivariate record data is considered as the general inference problem. Assume that the process of observing k records is repeated m times, independently. The asymptotic properties including consistency and asymptotic normality of the Maximum Likelihood (ML) estimates of parameters of the underlying distribution is then established, when m is ...

Asymptotic Distribution of Divergence Measure with Applications