Properties and characterization results based on discrete normal and discrete laplace distributions

We consider the class of discrete distributions supported on the set of integers Z = {0,±1,±2,…} and specified properties of them, especially discrete normal and discrete Laplace distributions. A discrete version of normal distribution is characterized via the solution of the normal distribution is characterized by maximum entropy when specified mean and variance on integer support on R. Following Kemp (1997), this distribution is characterized by the difference of two Hiene distributions. Bilateral power series distributions has maximum entropy when the kth factorial moment and mean are prescribed, the special case for k=2 is discrete normal. It will be shown that under such parameterizations, uniformly for all sufficiently large variance and all expectations, discrete normal and their two moments are given in very simple formula in view of the continuous case. we are going to derive several properties of discrete normal distributions via reparameterization. Approximating some moments for sum of two independent discrete normal distributions and noting on these distributions retains many of the nice features of the continuous normal distribution. Some results and characterizations for this model related to reliability measure (hazard rate, residual life, truncated mean), Fisher information, analogue of Fisher information, information measures, Jacobi series, common properties (for normal, discrete normal and Poisson distributions), results due to statistical aspects and some numerical calculations that also discussed here, lead us to another direction of this paper. Discrete version of the Laplace distribution and properties like, unimodality, infinite divisibility, closure properties w.r.t. geometric distribution, reliability measures, maximum entropy and information measures and finding analogue of properties of continuous Laplace distributions are derived. Finding the values of p(X>Y) regarding two independent random variables X and Y related to these two discrete distributions is another useful measure that studied at the end of this paper.

کلیدواژه ها:

Discrete Normal ، Discrete Laplace ، Entropy ، Fisher Information ، Reliability ، Chracterization.