Starting from on a recently introduced Gaussian class bivariate Weibull stochastic model, the probability density and the cumulative distribution functions of the product (Z1 Z2) c and the ratio (Z1/Z2) c, when Z1 and Z2 are correlated Weibull random variables belonging to this class (c > 0), are derived in closed form. Moreover, using the inequality between arithmetic and geometric mean, a uni...

In this paper, we propose to include Weibull tail-distributions in a more general family of distributions. In particular, the considered model also encompasses the whole Fréchet maximum domain of attraction as well as log-Weibull tail-distributions. The asymptotic normality of some tail estimators based on the log-spacings between the largest order statistics is established in a unified way wit...

t A mixture parametric model is used to analyze the changing pattern of Taiwanese mortality from 1926 to 1991. Three different age ranges are modeled as mixtures of extreme value distributions, namely the Weibull, inverse Weibull, and Gompertz distributions. The results show a significant improvement of mortality over the years.

Modifying the existing probability models in literature and introducing new extensions of is a prominent interesting research topic. However, most recent era, via trigonometry methods have received great attention. This paper also offers novel trigonometric version Weibull model called alpha power cosine-Weibull (for short, “NACos-Weibull”) distribution. The NACos-Weibull distribution introduce...

Abstract: A generalized version of four parameter modified inverse weibull distribution (MIWD) is introduced in this paper. This distribution generalizes the following distributions: (1) Modified Inverse exponential distribution, (2) Modified Inverse Rayleigh distribution, (3) Inverse weibull distribution. We provide a comprehensive description of the mathematical properties of the modified inv...

In this paper we will develop further the sequential life test approach presented in a previous article by [1] using an underlying two parameter Weibull sampling distribution. The minimum life will be considered equal to zero. We will again provide rules for making one of the three possible decisions as each observation becomes available; that is: accept the null hypothesis H0; reject the null ...

Weibull mixtures have been used extensively in reliability and survival analysis, and they have also been generalized by allowing negative mixing weights, which arise naturally under the formation of some structures of reliability systems. These models provide exible distributions for modelling dependent lifetimes from heterogeneous populations. In this paper, we study conditions on the mixing ...