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In this paper we are interested in the joint distribution of two order statistics from overlapping samples. We give an explicit formula for the distribution of such a pair of random variables under the assumption that the parent…
This paper presents a new methodology for generating continuous statistical distributions, integrating the exponentiated odds ratio within the framework of survival analysis. This new method enhances the flexibility and adaptability of…
This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson…
This expository note describes how to apply the method of maximum likelihood to estimate the parameters of the ``$q$-exponential'' distributions introduced by Tsallis and collaborators. It also describes the relationship of these…
Extended geometric distribution is defined and its mixture is characterized by the property of having completely monotone probability sequence. Also, convolution equations and probability generating functions are used to characterize…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
The statistical duality of distributions is a powerful tool for statistical inferences. In the paper the statistical duality of Laplace distribution is discussed. As shown the confidence density of the parameter of this distribution is…
The Transformed-Transformer family of distributions are the resulting family of distributions as transformed from a random variable $T$ through another transformer random variable $X$ using a weight function $\omega$ of the cumulative…
This article considers exponential families of truncated multivariate normal distributions with one-sided truncation for some or all coordinates. We observe that if all components are one-sided truncated then this family is not full. The…
The likelihood function is central to both frequentist and Bayesian formulations of parametric statistical inference, and large-sample approximations to the sampling distributions of estimators and test statistics, and to posterior…
This article aims to introduced a new distribution named as extended xgamma (EXg) distribution. This generalization is derived from xgamma distribution (Xg), a special finite mixture of exponential and gamma distributions [see, Sen et al.…
The main aim of this article is to characterize and investigate the three parameter exponentiated exponential Poisson probability distribution ${\rm EEP}(\alpha, \beta, \lambda)$ by giving explicit closed form expressions for its…
Consider a random sample $X_1 , X_2 , ..., X_n$ drawn independently and identically distributed from some known sampling distribution $P_X$. Let $X_{(1)} \le X_{(2)} \le ... \le X_{(n)}$ represent the order statistics of the sample. The…
We investigate a recursively generated sequence of random variables that begins with an Exponential random variable with parameter (i.e., inverse-mean) 1, and continues with additional Exponentials, each of whose random parameter possesses…
The aim of this paper, is to define a bivariate exponentiated generalized linear exponential distribution based on Marshall-Olkin shock model. Statistical and reliability properties of this distribution are discussed. This includes…
In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function.…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
Consider a probability distribution subordinate to a subexponential distribution with finite mean. In this paper, we discuss the second order tail behavior of the subordinated distribution within a rather general framework in which we do…
Many existing approaches for estimating parameters in settings with distributional shifts operate under an invariance assumption. For example, under covariate shift, it is assumed that $p(y|x)$ remains invariant. We refer to such…
We consider the distribution of the turning point location of time series modeled as the sum of deterministic trend plus random noise. If the variables are modeled by shifted exponentials, whose location parameters define the trend, we…