In this paper, general classes of probability distributions are characterized using the independence of suitable transformations of records in a sequence of independent, identically distributed random variables. Examples of special cases of general classes as Gumbel, Fréchet, Weibull, exponential and lognormal distributions are discussed. Further we use the theoretical results for application t...

Best practice life expectancy has recently been modeled using extreme value theory. In this paper we present the Gumbel autoregressive model of order one—Gumbel AR(1)—as an option for modeling best expectancy. This class represents a neat and coherent framework time series extremes. The distribution accounts nature expectancy, while AR structure temporal dependence in series. Model diagnostics ...

A new family of distributions called the Kumaraswamy Rayleigh is defied and studied. Some its relevant statistical properties are derived. Many bivariate type G families using Farlie-Gumbel-Morgenstern, modified Farlie-Gumbel-Morgenstern copula, Clayton copula Renyi’s entropy The method maximum likelihood estimation used. special models based on log-logistic, exponential, Weibull, Rayleigh, Par...

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.

We consider a discrete-time insurance risk model, in which the financial risks constitute a stationary process with finite dimensional distributions of Farlie–Gumbel–Morgenstern type. We obtain an exact asymptotic formula for the ruin probability, reflecting the impact of this kind of association structure among the financial risks. r 2007 Elsevier B.V. All rights reserved.

This paper provides new properties for tails of probability distributions belonging to a class defined according to the asymptotic decay of the tails. This class contains the one of regularly varying tails of distributions. The main results concern the relation between this larger class and the maximum domains of attraction of Fréchet and Gumbel.

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...