Motivated by Finner et al. (2008), the asymptotic behavior of the probability density function (pdf) and the cumulative distribution function (cdf) of the generalized exponential and Maxwell distributions are studied. Specially, we consider the asymptotic behavior of the ratio of the pdfs (cdfs) of the generalized exponential and Student's $t$-distributions (likewise for the Maxwell and Student's $t$-distributions) as the degrees of freedom parameter approach infinity in an appropriate way. As by products, Mills' ratios for the generalized exponential and Maxwell distributions are gained. Moreover, we illustrate some examples to indicate the application of our results in extreme value theory.
Comments: 9 Pages.
[v1] 2014-09-15 10:24:34
Unique-IP document downloads: 78 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.