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Theory & Methods: Exact Short Confidence Intervals from Discrete Data
Author(s) -
Kabaila Paul,
Byrne John
Publication year - 2001
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00177
Subject(s) - mathematics , infimum and supremum , confidence interval , binomial proportion confidence interval , cdf based nonparametric confidence interval , coverage probability , probability mass function , tolerance interval , confidence distribution , statistics , random variable , binomial (polynomial) , interval (graph theory) , credible interval , robust confidence intervals , upper and lower bounds , negative binomial distribution , combinatorics , mathematical analysis , poisson distribution
Suppose that X is a discrete random variable whose possible values are {0, 1, 2,⋯} and whose probability mass function belongs to a family indexed by the scalar parameter θ . This paper presents a new algorithm for finding a 1 − α confidence interval for θ based on X which possesses the following three properties: (i) the infimum over θ of the coverage probability is 1 − α ; (ii) the confidence interval cannot be shortened without violating the coverage requirement; (iii) the lower and upper endpoints of the confidence intervals are increasing functions of the observed value x . This algorithm is applied to the particular case that X has a negative binomial distribution.