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In this paper we investigate the Burr distributions family which contains twelve members. Second order expansions of quantiles of the Burr's distributions are provided on which may be based statistical methods, in particular in extreme…
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…
Assumptions on a likelihood function, including a local Glivenko-Cantelli condition, imply the existence of M-estimators converging to an M-functional. Scatter matrix-valued estimators, defined on all empirical measures on ${\Bbb{R}}^d$ for…
This paper generalizes the notion of sufficiency for estimation problems beyond maximum likelihood. In particular, we consider estimation problems based on Jones et al. and Basu et al. likelihood functions that are popular among…
We study higher order expansions both in the Berry-Ess\'een estimate (Edgeworth expansions) and in the local limit theorems for Birkhoff sums of chaotic probability preserving dynamical systems. We establish general results under technical…
Maximum likelihood estimation of a location parameter fails when the density have unbounded mode. An alternative approach is considered by leaving out a data point to avoid the unbounded density in the full likelihood. This modification…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong…
The one-dimensional Dickman distribution arises in various stochastic models across number theory, combinatorics, physics, and biology. Recently, a definition of the multidimensional Dickman distribution has appeared in the literature,…
Some improved estimators of the location parameters of several exponential distributions with ordered restriction are derived and compared numerically using Monte Carlo simulations. Note that the two-parameter exponential distribution is…
We consider the Grenander estimator that is the maximum likelihood estimator for non-increasing densities. We prove uniform central limit theorems for certain subclasses of bounded variation functions and for H\"older balls of smoothness…
Stochastic ordering among distributions has been considered in a variety of scenarios. Economic studies often involve research about the ordering of investment strategies or social welfare. However, as noted in the literature, stochastic…
Generalized Maxwell distribution is an extension of the classic Maxwell distribution. In this paper, we concentrate on the joint distributional asymptotics of normalized maxima and minima. Under optimal normalizing constants, asymptotic…
We consider the precise upper large deviations estimates for the maximal displacement of a branching random walk. In addition, we obtain a description of the extremal process of the branching random walk conditioned on this large deviations…
In this report, we explore the data selection leading to a family of estimators maximizing a centrality. The family allows a nice properties leading to accurate and robust probability density function fitting according to some criteria we…
In this paper, we introduce a new class of bivariate distributions called the bivariate exponentiated extended Weibull distributions. The model introduced here is of Marshall-Olkin type. This new class of bivariate distributions contains…
The main goal of this research is to model and investigate generalizations of functions from [31]. Arguments of modeled functions are presented by the representation $\pi_{\mathfrak p}$ from [22].
Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
Here, we introduce a new class of Lindley generated distributions which results in more flexible model with increasing failure rate (IFR), decreasing failure rate(DFR) and up-side down hazard functions for different choices of parametric…