Physical Sciences and Mathematics Commons^™

On Approximating Point Spread Distributions, Tamas Lengyel

Tamas Lengyel

We discuss some properties of the point spread distribution, defined as the distribution of the difference of two independent binomial random variables with the same parameter n in- cluding exact and approximate probabilities and related optimization issues. We use various approximation techniques for different distributions, special functions, and analytic, combi- natorial and symbolic methods, such as multi-summation techniques. We prove that in case of unequal success rates, if these rates change with their difference kept fix and small, and n is appropriately bounded, then the point spread distribution only slightly changes for small point differences. We also prove that for …