Moment Recurrence Relations for Binomial, Poisson and Hypergeometric Frequency Distributions

Testing Poisson Binomial Distributions

A Poisson Binomial distribution over n variables is the distribution of the sum of n independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution P supported on {0, . . . , n} to which we have sample access is a Poisson Binomial distribution, or far from all Poisson Binomial distributions. The sample complexity of our algorithm is O(n) to which we provid...

Recurrence Relations for Moment Generating Functions of Generalized Order Statistics Based on Doubly Truncated Class of Distributions

In this paper, we derived recurrence relations for joint moment generating functions of nonadjacent generalized order statistics (GOS) of random samples drawn from doubly truncated class of continuous distributions. Recurrence relations for joint moments of nonadjacent GOS (ordinary order statistics (OOS) and k-upper records (k-RVs) as special cases) are obtained. Single and product moment gene...

Confidence Bounds & Intervals for Parameters Relating to the Binomial, Negative Binomial, Poisson and Hypergeometric Distributions With Applications to Rare Events

We present here by direct argument the classical Clopper-Pearson (1934) “exact” confidence bounds and corresponding intervals for the parameter p of the binomial distribution. The same arguments can be applied to derive confidence bounds and intervals for the negative binomial parameter p, for the Poisson parameter λ, for the ratio of two Poisson parameters, ρ = λ1/λ2, and for the parameter D o...

On the quantile transform for asymmetric binomial and hypergeometric distributions

Recurrence Relations for Quotient Moment of Generalized Pareto Distribution Based on Generalized Order Statistics and Characterization

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In this paper, we established exact expressions and recurrence relations satisfied by the quotient moments of generalized order statistic...