Tail behavior of the generalized exponential and Maxwell distributions ∗
نویسندگان
چکیده
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.
منابع مشابه
On Bivariate Generalized Exponential-Power Series Class of Distributions
In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains the bivariate generalized exponential-Poisson, bivariate generalized exponential-logarithmic, bivariate generalized exponential-binomial and bivariate generalized exponential-negative binomial distributions as specia...
متن کاملStatistical Modeling for Oblique Collision of Nano and Micro Droplets in Plasma Spray Processes
Spreading and coating of nano and micro droplets on solid surfaces is important in a wide variety of applications including plasma spray coating, ink jet printing, DNA synthesis and etc. In spraying processes, most of droplets collide obliquely to the surface. The purpose of this article is to study the distribution of nano and micro droplets spreading when droplets impact at an oblique a...
متن کاملOn Exponential Power Distribution And Poultry Feeds Data: A Case Study
Abstract. In this paper, we propose to study a generalized form of the exponential power distribution which contains others in the literature as special cases. This unifying exponential power distribution is characterized by a parameter ω and a function h(ω) which regulates the tail behavior of the distribution, thus making it more flexible and suitable for modeling than the usual normal di...
متن کاملA New Class of Distributions Based on Hurwitz Zeta Function with Applications for Risk Management
Notice that the Riemann Zeta function is simply ζ(s, 1) = ζ(s). In the next section we provide a new family of distributions, the Zeta family, which is based on the Hurwitz Zeta function, and provide its characteristic function. We also show that the well known generalized gamma family of distributions is a special case of the proposed family. (Notice that the exponential power family of distri...
متن کاملThe Tail Mean-Variance Model and Extended Efficient Frontier
In portfolio theory, it is well-known that the distributions of stock returns often have non-Gaussian characteristics. Therefore, we need non-symmetric distributions for modeling and accurate analysis of actuarial data. For this purpose and optimal portfolio selection, we use the Tail Mean-Variance (TMV) model, which focuses on the rare risks but high losses and usually happens in the tail of r...
متن کامل