Monotonicity in the Sample Size of the Length of Classical Confidence Intervals

TL;DR

This paper proves that the average length of classical confidence intervals for gamma and normal distribution parameters decreases monotonically as the sample size increases, using properties of the gamma function.

Contribution

It establishes a monotonicity property of confidence interval lengths with respect to sample size for gamma and normal distributions, based on gamma function properties.

Findings

Average length decreases monotonically with sample size

Results apply to gamma and normal distribution parameters

Uses properties of the gamma function for proofs

Abstract

It is proved that the average length of standard confidence intervals for parameters of gamma and normal distributions monotonically decrease with the sample size. The proofs are based on fine properties of the classical gamma function.