Bounds on tail probabilities for negative binomial distributions

@article{Harremoës2016,
abstract = {In this paper we derive various bounds on tail probabilities of distributions for which the generated exponential family has a linear or quadratic variance function. The main result is an inequality relating the signed log-likelihood of a negative binomial distribution with the signed log-likelihood of a Gamma distribution. This bound leads to a new bound on the signed log-likelihood of a binomial distribution compared with a Poisson distribution that can be used to prove an intersection property of the signed log-likelihood of a binomial distribution compared with a standard Gaussian distribution. All the derived inequalities are related and they are all of a qualitative nature that can be formulated via stochastic domination or a certain intersection property.},
author = {Harremoës, Peter},
journal = {Kybernetika},
keywords = {tail probability; exponential family; signed log-likelihood; variance function; inequalities},
language = {eng},
number = {6},
pages = {943-966},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Bounds on tail probabilities for negative binomial distributions},
url = {http://eudml.org/doc/287922},
volume = {52},
year = {2016},
}

TY - JOUR
AU - Harremoës, Peter
TI - Bounds on tail probabilities for negative binomial distributions
JO - Kybernetika
PY - 2016
PB - Institute of Information Theory and Automation AS CR
VL - 52
IS - 6
SP - 943
EP - 966
AB - In this paper we derive various bounds on tail probabilities of distributions for which the generated exponential family has a linear or quadratic variance function. The main result is an inequality relating the signed log-likelihood of a negative binomial distribution with the signed log-likelihood of a Gamma distribution. This bound leads to a new bound on the signed log-likelihood of a binomial distribution compared with a Poisson distribution that can be used to prove an intersection property of the signed log-likelihood of a binomial distribution compared with a standard Gaussian distribution. All the derived inequalities are related and they are all of a qualitative nature that can be formulated via stochastic domination or a certain intersection property.
LA - eng
KW - tail probability; exponential family; signed log-likelihood; variance function; inequalities
UR - http://eudml.org/doc/287922
ER -