A confidence interval for the population mean of a one-parameter exponential distribution based on the Wilson-Hilferty transformation

Abstract

In this paper, an approximate confidence interval (CI) is proposed for the population mean of a one-parameter exponential distribution. The Wilson-Hilferty approximation is used to transform the exponential random variable to a normal random variable. The efficiency of this proposed confidence interval is evaluated using an extensive Monte-Carlo simulation study. Through this method, the coverage probabilities and average widths of the proposed CI are compared with those of the other two commonly existing CIs, namely, the exact and asymptotic confidence intervals. The simulation results show that the proposed confidence interval performs well in terms of coverage probability and average width. Additionally, the average width of the proposed confidence interval is lower than that of the asymptotic confidence interval for a small sample size and all levels of the parameter ( $\theta$ ). Furthermore, the three confidence interval estimations get systematically closer to the nominal level for all levels of the sample size and parameter. In addition, the efficiencies of the three confidence interval estimations seem to have no difference for a large sample size and all levels of the parameter. Real-life data was used for illustration and performing a comparison that support the findings obtained from the simulation study.

Keywords

Confidence interval exponential distribution Wilson-Hilferty transformation normal distribution coverage probability average width

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