Theory & Methods: Exact Short Confidence Intervals from Discrete Data
Paul V. Kabaila, John Byrne · Australian & New Zealand Journal of Statistics · 2001
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.