In this paper, a discrete Poisson-Garima distribution has been obtained by compounding Poisson distribution with Garima distribution introduced by Shanker [1]. The general expression for the th factorial moment has been derived and hence moments about origin and central moments have been obtained. The expression for coefficient of Variation, skewness, kurtosis and index of dispersion has been g...

In this study, we have considered a series system composed of stochastically independent M-component where M is a random variable having the zero truncated modified discrete Lindley distribution. This distribution is newly introduced by transforming on original parameter. The properties of the distribution of the lifetime of above system have been examined under the given circumstances and also...

this paper investigates a discrete-time impatient customer queue with bernoulli-schedule vacation interruption. the  vacation times and the service times during regular busy period and during working vacation period are assumed to follow geometric distribution. we obtain the steady-state probabilities at arbitrary and outside observer's observation epochs using recursive technique. cost an...

Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a large class of probability models through empirical counts of certain patterns in a graph. We establish some general asymptotic properties of empirical graph...

In this note, two characterizations of the exponential distribution are established. Theorem 1: Let a > -1, a ~ O. A positive random variable X has an exponential distribution if and only if E[CX-y)aI X > y] is a finite constant for all y ~ O. Theorem 2: Let Xl ,X2, ..• ,Xn be i.i.d. random variables having a continuous distribution FCx), and XCl)'XC2)' ... 'XCn) their order statistics. Let a >...

The collection and analysis of user data drives improvements in the app and web ecosystems, but comes with risks to privacy. This paper examines discrete distribution estimation under local privacy, a setting wherein service providers can learn the distribution of a categorical statistic of interest without collecting the underlying data. We present new mechanisms, including hashed k-ary Random...

as the equation for the spaces of generalized functions. Making use of the fundamental solution of the heat equation we solve the general solutions and the stability problems of this equation in the spaces of tempered distributions and Fourier hyperfunctions. Moreover, using the regularizing functions, we extend these results to the space of distributions. 2000 MSC: 39B82; 46F05.

We consider the problem of discrete distribution estimation under l1 loss. We provide tight upper and lower bounds on the maximum risk of the empirical distribution (the maximum likelihood estimator), and the minimax risk in regimes where the support size S may grow with the number of observations n. We show that among distributions with bounded entropy H , the asymptotic maximum risk for the e...

The Selberg trace formula leads naturally to the study of certain tempered distributions on reductive groups defined over local fields. An important problem is to calculate the Fourier transforms of these distributions. We shall consider this question for the case tha t the local field is R and the group G is semisimple and has real rank one. In this context the notion of the Fourier transform ...

A class of random discrete distributions P is introduced by means of a recursive splitting of unity. Assuming supercritical branching, we show that for partitions induced by sampling from such P a power growth of the number of blocks is typical. Some known and some new partition structures appear when P is induced by a Dirichlet splitting. AMS 2000 subject classifications: Primary 60G09, 60C05