Due to the advance computer technology, use of probability distributions has been raised up solve real life problems. These applications are found in reliability engineering, sciences, economics, psychology, survival analysis, and some others. This study offers a new model called Marshall–Olkin Extended Gumbel Type-II (MOEGT-II) which can various shapes failure rate function. The proposed distr...

A copula is a useful tool for constructing bivariate and/or multivariate distributions. In this article, we consider a new modified class of FGM (Farlie–Gumbel–Morgenstern) bivariate copula for constructing several different bivariate Kumaraswamy type copulas and discuss their structural properties, including dependence structures. It is established that construction of bivariate distributions ...

We show that the exact distribution of a positive linear combination of independent Gumbel random variables can be written as the sum of a linear combination of independent log Gamma distributions, and an independent shifted Generalized Integer Gamma distribution. Given the complexity of this exact distribution, we develop a near-exact distribution using a shifted Generalized Near-Integer Gamma...

In this paper we study the asymptotic behavior of the tail probabilities of sums of dependent and real-valued random variables whose distributions are assumed to be subexponential and not necessarily of dominated variation. We propose two general dependence assumptions under which the asymptotic behavior of the tail probabilities of the sums is the same as that in the independent case. In parti...

We consider local alignments without gaps of two independent Markov chains from a finite alphabet, and we derive sufficient conditions for the number of essentially different local alignments with a score exceeding a high threshold to be asymptotically Poisson distributed. From the Poisson approximation a Gumbel approximation of the maximal local alignment score is obtained. The results extend ...

This paper discusses the application of extreme events distribution taking the Limpopo River Basin at Xai-Xai station, in Mozambique, as a case analysis. We analyze the extreme value concepts, namely Gumbel, Fréchet, Weibull and Generalized Extreme Value Distributions and then extrapolate the original data to 1000, 5000 and 10000 figures for further simulations and we compare their outcomes bas...

In this paper, we study the estimation problems for the two-parameter exponentiated Gumbel distribution based on lower record values. An exact confidence interval and an exact joint confidence region for the parameters are constructed. A simulation study is conducted to study the performance of the proposed confidence interval and region. Finally, a numerical example with real data set is given...

Abstract: In this paper we consider various Marshall-Olkin distributions and develop autoregressive minification processes with stationary marginals as exponential, Weibull, uniform, Pareto, Gumbel, Lomax etc. The applications in reliability modelling and stress-strength analysis are considered.Problems of estimation of parameters is addressed. Various properties are examined. Modelling with re...

Correspondence analysis is a multivariate technique used to visualize categorical data, usually data in a two-way contingency table. Some extensions of correspondence analysis to a continuous bivariate distribution are presented, rstly from a canonical correlation analysis perspective and then from a continuous scaling perspective. These extensions are applied to the Farlie-Gumbel-Morgenstern (...

Extreme value theory for a class of stochastic volatility models, in which the logarithm of the conditional variance follows a Gaussian linear process, is developed. A result for the asymptotic tail behavior of the transformed stochastic volatility process is established and used to prove that the suitably normalized extremes converge in distribution to the double exponential (Gumbel) distribut...