Abstract. Let (X, Y ) be a bivariate elliptical random vector with associated random radius in the Gumbel maxdomain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability P{X > x, Y > y} for x, y large. Further, based on the asymptotic bounds we discuss some aspects of the statistical modelling of joint survival probabilities and the surviva...

The recent work “Bringing closure to the plotting position controversy” (Makkonen, 2008a) states the impossibility of a different solution from the classical plotting position proposed by Weibull (1939) and promoted by Gumbel (1958). In this paper, a new and better distribution-free solution is obtained via axiomatic approach. The applicative implications of a comparative study, carried out by ...

We provide a combinatorial description of exclusion statistics in terms of minimal difference p partitions. We compute the probability distribution of the number of parts in a random minimal p partition. It is shown that the bosonic point p = 0 is a repulsive fixed point for which the limiting distribution has a Gumbel form. For all positive p the distribution is shown to be Gaussian. PACS numb...

Consider the MLEs (maximum likelihood estimators) of the parameters of the Gumbel distribution using SRS (simple random sample) and RSS (ranked set sample) and the MOMEs (method of moment estimators) and REGs (regression estimators) based on SRS. A comparison between these estimators using bias and MSE (mean square error) was performed using simulation. It appears that the MLE based on RSS can ...

‎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...

    In this research in order to frequency analysis of maximum daily rainfall in various climates of Iran the data of 40 synoptic rain gauges collected in 40 years period i.e., 1973 to 2012 were used. These stations are located in various climates of Iran according to De Martonne climatic classification. At first, input of data to HYFA package was performed. The mentioned package includes seven...

The Gumbel model is a very popular statistical due to its wide applicability for instance in the course of certain survival, environmental, financial or reliability studies. In this work, we have introduced bimodal generalization distribution thatcan be an alternative data. We derive analytical shapes corresponding probability density function and thehazard rate provide graphical illustrations....