Asymptotic confidence interval for the coefficient of variation of Poisson distribution: a simulation study

Abstract

A new asymptotic confidence interval constructed by using a confidence intervalfor the Poisson mean is proposed for the coefficient of variation of the Poisson distribution.The following confidence intervals are considered: McKay’s confidence interval, Vangel’sconfidence interval and the proposed confidence interval. Using Monte Carlo simulations,the coverage probabilities and expected lengths of these confidence intervals are compared.Simulation results show that all scenarios of the new asymptotic confidence interval havedesired minimum coverage probabilities of 0.95 and 0.90. In addition, the newly proposedconfidence interval is better than the existing ones in terms of coverage probability andexpected length for all sample sizes and parameter values considered in this paper.

Keywords

• coefficient of variation
• confidence interval
• coverage probability
• expected length
• Poisson distribution