The estimate of $\chi^2$-distance between binomial and generalized binomial distributions

GENERALIZED BINOMIAL AND NEGATIVE BINOMIAL DISTRIBUTIONS OF ORDER k BY THE/-OVERLAPPING ENUMERATION SCHEME

A b s t r a c t . In this paper, we investigate the exact distribution of the waiting time for the r-th t-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of order k and an extended Poisson distr...

Binomial and multinomial 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...

Characteristics of the Temporal Behavior of Entanglement between Photonic Binomial Distributions and a Two-Level Atom in a Damping Cavity

In the present study, temporal behavior of entanglement between photonic binomial distributions and a two-level atom in a leaky cavity, in equilibrium with the environment at a temperature T, is studied. In this regard, the master equation is solved in the secular approximation for the density matrix, when the initial photonic distribution is binomial, while the atomic states obey the Boltzmann...

Multiplicity Distributions in Strong Interactions: a Generalized Negative Binomial Model

A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in totaland limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of the KNO scaling function derived in Polyakov’s similarity hypothesis for strong interactions as well as in perturbative QCD, ψ(z) ∝ zα exp(−zμ). Various chara...