A new flexible univariate probability distribution was defined in this paper. The is so called the ‘exponentiated Gumbel–Weibull {logistic} distribution’ and it arose by using exponentiated Gumbel to generate a generalized Weibull logit function or quantile of logistic as link. observed be both unimodal bimodal well exhibits various shape tail properties consistent with data arising from severa...

We investigate the maximal non-critical cluster in a big box in various percolation-type models. We investigate its typical size, and the fluctuations around this typical size. The limit law of these fluctuations are related to maxima of independent random variable with law described by a single cluster. Key-words: Maximal clusters, exponential law, Gumbel distribution, FKG inequality, second m...

‎The complex system containing n elements‎, ‎each having three dependent components‎, ‎is described‎. ‎The reliability function of such systems is investigated using a trivariate binomial model‎. ‎In addition‎, ‎the mean residual life function of a complex system with intact components at time t is derived‎. ‎The results are simplified for a t...

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...

The classical Gumbel probability distribution is modified in order to study the failure times of a given system. Bayesian estimates of the reliability function under five different parametric priors and the square error loss are studied. The Bayesian reliability estimate under the non-parametric kernel density prior is compared with those under the parametric priors and numerical computations a...

Abstract: Let X be a generalised symmetrised Dirichlet random vector inIR, k ≥ 2, and let tn ∈IRk, n ≥ 1 be such that limn→∞ P {X > tn} = 0. In this paper we derive an exact asymptotic expansion of P {X > tn} as n → ∞, assuming that the associated random radius of X has distribution function in the Gumbel max-domain of attraction.