Related papers: New generalized unit distributions based on order …
The generalized logistic equation is derived to model kinetics and statistics of natural processes such as earthquakes, forest fires, floods, landslides, and many others. The general solution of this equation for q=1 is a product of an…
Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme…
In this paper some new characterizing theorems of exponential distribution based on order statistics are presented. Some existing results are generalized and the open conjecture by Arnold and Villasenor is solved.
The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost of the formula in the case of two…
In this paper, we consider the order statistics from a newly-introduced lifetime distribution called the XLindley distribution. We have derived explicit closed form expressions for the single moments and product moments of order statistics…
Some results on the ordered statistics of eigenvalues for one-dimensional random Schr\"odinger Hamiltonians are reviewed. In the case of supersymmetric quantum mechanics with disorder, the existence of low energy delocalized states induces…
Let $\{X_{n}, n\ge 1\}$ be a sequence of independent random variables with common general error distribution $GED(v)$ with shape parameter $v>0$, and let $M_{n,r}$ denote the $r$th largest order statistics of $X_{1}, X_{2}, \cdots, X_{n}$.…
A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…
The Median Based Unit Weibull is a new 2 parameter unit Weibull distribution defined on the unit interval (0,1). Estimation of the parameters using MLE encountered some problems like large variance. Using generalized method of moments…
Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…
Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval…
In this paper, we consider objective Bayesian inference of the generalized exponential distribution using the independence Jeffreys prior and validate the propriety of the posterior distribution under a family of structured priors. We…
Rank-ordering statistics provides a perspective on the rare, largest elements of a population, whereas the statistics of cumulative distributions are dominated by the more numerous small events. The exponent of a power law distribution can…
The Lindley distribution was first introduced by Lindley in 1958 for Bayesian computations. Over the past years, various generalizations of this distribution have been proposed by different authors. The generalized Lindley distributions…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a…
Several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. Recently, a new generalization of…
In this paper, we have studied the stochastic comparisons of the highest and lowest order statistics of exponentiated Gumble type-II distribution with three parameters. We have compared both the statistics by using three different…
In statistical analysis, quantifying uncertainties through measures such as entropy, extropy, varentropy, and varextropy is of fundamental importance for understanding distribution functions. This paper investigates several properties of…
In [3], we have introduced a probability measure to study the power and exponential sums for a certain coding system. The distribution function of the probability measure gives explicit formulas for the power and exponential sums.…