Related papers: On a six-parameter generalized Burr XII distributi…
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…
The hypergeometric distribution is a popular distribution, whose properties have been extensively investigated. Generating functions of this distribution, such as the probability-generating function, the moment-generating function, and the…
We propose results of the investigation of properties of the random sums of random variables. We consider the case, where the number of summands is the first moment of an event occurrence. An integral equation is presented that determines…
We introduce in this paper a new generalization of the flexible Weibull distribution with four parameters. This model based on the Beta generalized (BG) distribution, Eugene et al. \cite{Eugeneetal2002}, they first using the BG distribution…
In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in [1], which addressed…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
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.…
We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…
We study the probability distribution $P$ of the sum of a large number of non-identically distributed random variables $n_m$. Condensation of fluctuations, the phenomenon whereby one of such variables provides a macroscopic contribution to…
An expression for the joint probability distribution of the principal curvatures at an arbitrary point in the ensemble of isosurfaces defined on isotropic Gaussian random fields on Rn is derived. The result is obtained by deriving symmetry…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product $XY$ is derived. Some basic distributional properties are also derived, including…
Probability distributions supported on the simplex enjoy a wide range of applications across statistics and machine learning. Recently, a novel family of such distributions has been discovered: the continuous categorical. This family enjoys…
Based on the generalized Boltzmann equation and the reverse function of the distribution function, we investigate the two-parameter generalized statistics and get an expression between the two parameters (k,r) and the physical quantities…
In this study an attempt has been made to propose a way to develop new distribution. For this purpose, we need only idea about distribution function. Some important statistical properties of the new distribution like moments, cumulants,…
The normal distribution has the unique property that the cumulant generating function has only two terms, namely those involving the mean and the variance. This property is used to construct a simple by using the log of the modulus of the…
We study the non-stationary Feller process with time varying coefficients. We obtain the exact probability distribution exemplified by its characteristic function and cumulants. In some particular cases we exactly invert the distribution…
The Wishart distribution and its generalizations are among the most prominent probability distributions in multivariate statistical analysis, arising naturally in applied research and as a basis for theoretical models. In this paper, we…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
In this paper we introduce a new probability distribution on (0,1), associated with the I-function, namely, the I-function distribution. This distribution generalizes several known distributions with positive support. It is also shown that…
We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schrodinger equation. The…