On confidence bounds for one-parameter exponential families

ABSTRACT

There exist various methods for providing confidence intervals for unknown parameters of interest on the basis of a random sample. Generally, the bounds are derived from a system of non-linear equations. In this article, we present a general solution to obtain an unbiased confidence interval with confidence coefficient 1 − α in one-parameter exponential families. Also we discuss two Bayesian credible intervals, the highest posterior density (HPD) and relative surprise (RS) credible intervals. Standard criteria like the coverage length and coverage probability are used to assess the performance of the HPD and RS credible intervals. Simulation studies and real data applications are presented for illustrative purposes.

Keywords:

• Coverage length
• Coverage probability
• HPD credible interval
• One-parameter exponential family
• Pivotal quantity method
• Relative surprise credible interval
• Unbiased confidence interval

Mathematics Subject Classification:

• 62F15
• 62F25