Related papers: Exponential and Hypoexponential Distributions: Som…
The sum of independent, but not necessary identically distributed, exponential random variables follows hypoexponential distribution. We focus on a particular case when all, but one rate parameters of the exponential variables are…
There are given characterizations of the exponential distribution by the properties of the independence of linear forms with random coefficients. Related results based on the constancy of regression of one statistic on a linear form are…
In this paper we study the Exponentiated Hypoexponential Distribution with different parameters. The distribution added a parameter to the n parameters of the Hypoexponenial distribution. We first derive a closed expression of the…
It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are…
Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent random variables (not necessarily identically distributed), and $\eta$ be a counting random variable independent of this sequence. We obtain sufficient conditions on…
We characterize the exponential distribution as the only one which satisfies a regression condition. This condition involves the regression function of a fixed record value given two other record values, one of them being previous and the…
Let $X_1, X_2,\ldots, X_n$ be $n$ independent and identically distributed random variables, here $n \geq 2.$ Let $X_{(1)}, X_{(2)}, \ldots, X_{(n)}$ be the order statistics of $X_1, X_2,..., X_n.$ In this note we proved that: (I) If $X_1,…
A random phenomenon may have two sources of random variation: an unstable identity and a set of external variation-generating factors. When only a single source is active, two mutually exclusive extreme scenarios may ensue that result in…
It is shown that the exponential is the only distribution which satisfies a certain regression equation. This characterization equation involves the conditional expectation (regression function) of a record value given a pair of record…
A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…
A random variable is equi-dispersed if its mean equals its variance. A Poisson distribution is a classical example of this phenomenon. However, a less well-known fact is that the class of normal densities that are equi-dispersed constitutes…
We prove the following exponential inequality: Let $n\geq 1$ and let $X_1,...,X_n$ be $n$ independent identically distributed symmetric real-valued random variables. For any $x,y>0$, we have \[\mathbb{P}\big({X_1+...+X_n}\geq x,\,…
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…
A characterization of the exponential distribution based on equidistribution conditions for maxima of random samples with consecutive sizes n-1 and n for an arbitrary and fixed n>2 is proved. This solves an open problem stated recently in…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
Let $S_n$ be the sum of independent random variables with distribution $F$. Under the assumption that $-\log(1-F(x))$ is slowly varying, conditions for $$ \lim_{n\to\infty}\sup_{s\ge t_n}\left|{P[S_n>s]\over n(1-F(s))}-1\right| =0 $$ are…
We characterize the exponential distribution in terms of the regression of a record value with non-adjacent record values as covariates. We also study characterizations based on the regression of linear combinations of record values.
The class of subweibull distributions has recently been shown to generalize the important properties of subexponential and subgaussian random variables. We describe alternative characterizations of subweibull distributions and detail the…