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Saddlepoint approximations for the sum of independent non‐identically distributed binomial random variables
Author(s) -
Eisinga Rob,
Te Grotenhuis Manfred,
Pelzer Ben
Publication year - 2013
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12002
Subject(s) - independent and identically distributed random variables , mathematics , random variable , binomial distribution , binomial (polynomial) , negative binomial distribution , cumulative distribution function , binomial approximation , sum of normally distributed random variables , compound poisson distribution , statistics , probability density function , poisson distribution , poisson regression , population , demography , sociology
We discuss saddlepoint approximations to the distribution of the sum of independent non‐identically distributed binomial random variables. We examine the accuracy of the saddlepoint methods for a sum of 10 binomials with different sets of parameter values. The numerical results indicate that the saddlepoint approximations provide very accurate estimates for the probability mass function and the right‐tail probabilities for the cumulative distribution function of the sum.