Related papers: The Three Extreme Value Distributions: An Introduc…
Weibull distribution has received a wide range of applications in engineering and science. The utility and usefulness of an estimator is highly subject to the field of practitioner's study. In practice users looking for their desired…
In this paper, we propose methods for the estimation of parameters for the three-parameter Reflected Weibull distribution. The Moment estimator , Maximum likelihood estimator and Location and Scale Parameters free maximum likelihood…
For a skew normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an…
This paper presents an initial exploration of high frequency records of extreme wind speed in two steps. The first consists in finding the suitable extreme distribution for $120$ measuring stations in Switzerland, by comparing three known…
A pedagogical account of some aspects of Extreme Value Statistics (EVS) is presented from the somewhat non-standard viewpoint of Large Deviation Theory. We address the following problem: given a set of $N$ i.i.d. random variables…
The fracture strength distribution of materials is often described in terms of the Weibull law which can be derived by using extreme value statistics if elastic interactions are ignored. Here, we consider explicitly the interplay between…
In this paper, we introduce a new distribution called Burr III-Weibull(BW) distribution using the concept of competing risk. We derive moments, conditional moments, mean deviation and quantiles of the proposed distribution. Also the Renyi's…
Extreme value distributions are routinely employed to assess risks connected to extreme events in a large number of applications. They typically are two- or three- parameter distributions: the inference can be unstable, which is…
We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed)…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the…
Using the proposed by us thinning approach to describe extreme matrices, we find an explicit exponentiation formula linking classical extreme laws of Fr\'echet, Gumbel and Weibull given by Fisher-Tippet-Gnedenko classification and free…
In extreme values theory, for a sufficiently large block size, the maxima distribution is approximated by the generalized extreme value (GEV) distribution. The GEV distribution is a family of continuous probability distributions, which has…
In algebraic statistics, the maximum likelihood degree of a statistical model refers to the number of solutions (counted with multiplicity) of the score equations over the complex field. In this paper, the maximum likelihood degree of the…
We consider the extreme eigenvalues of the sample covariance matrix $Q=YY^*$ under the generalized elliptical model that $Y=\Sigma^{1/2}XD.$ Here $\Sigma$ is a bounded $p \times p$ positive definite deterministic matrix representing the…
In this paper, we propose a new distribution with unitary support which can be characterized as a ratio of the type $W=X_1/(X_1+X_2)$, where $(X_1, X_2)^\top$ follows a bivariate extreme distribution with Fr\'echet margins, that is, $X_1$…
In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an…
In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that,…
The Weibull distribution is a very applicable model for the lifetime data. For inference about two Weibull distributions using records, the shape parameters of the distributions are usually considered equal. However, there is not an…
The Weibull--like distributions form a large class of probability distributions that belong to the domain of attraction for the maxima of the Gumbel law. Besides the Weibull distribution, it includes important distributions as the Gamma…