Related papers: Characterization of exponential distribution throu…
A new characterization of the exponential distribution is established. It is proven that the well-known Sukhatme-Renyi necessary condition is also sufficient for exponentiality. A method of proof due to Arnold and Villasenor based on the…
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.
Arnold and Villasenor (2013) obtain a series of characterizations of the exponential distribution based on random samples of size two. These results were already applied in constructing goodness-of-fit tests. Extending the techniques from…
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…
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…
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…
In this paper three new characterizing theorems of exponential distribution are presented. They are based on equidistribution of some functions of order statistics. All of them include the median of sample of size three.
The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the…
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…
We give a sufficient condition for a random sequence in [0,1] generated by a $\Psi$-process to be equidistributed. The condition is met by the canonical example -- the $\max$-2 process -- where the $n$th term is whichever of two uniformly…
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…
We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application…
In this paper non-asymptotic exact exponential estimates are derived for the tail of maximum distribution of random field in the terms of majoring measures or, equally, generic chaining.
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…
A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on…
It is well known that the independence of the sample mean and the sample variance characterizes the normal distribution. By using Anosov's theorem, we further investigate the analogous characteristic properties in terms of the sample mean…
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,…
Two old conjectures from problem sections, one of which from SIAM Review, concern the question of finding distributions that maximize P(Sn <= t), where Sn is the sum of i.i.d. random variables X1, ..., Xn on the interval [0,1], satisfying…
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…
A predictive distribution over a sequence of $N+1$ events is said to be "frequency mimicking" whenever the probability for the final event conditioned on the outcome of the first $N$ events equals the relative frequency of successes among…