Estimating the percentiles of some misspecified non-nested distributions ^*

^* The authors wish to thank an anonymous referee for helpful comments. The third author wishes to acknowledge the financial support of the Australian Research Council

Abstract

In this paper we assess the effects of misspecification in estimating the percentiles of the 2- and 3-parameter gamma, Weibull and lognormal distributions. In the experiments, the true model is either a 2- or 3-parameter distribution, the estimated quantities are the maximum observed value or the ninety-eighth percentile value, the performance criteria are the BIAS and RRMSE associated with the estimated quantities, and four misspecified non-nested alternative distributions are estimated. The 2- and 3-parameter versions of two non-nested distributions are estimated to examine the consequences of misspecifying the true distribution, namely estimating the 2- or 3-parameter distribution when a 2- or 3-parameter version of a non-nested distribution is correct. The shape parameter is examined over a range of possible values where the density functions are positively skewed. When the 2- or 3-parameter gamma distribution is true, the 3-parameter Weibull distribution is found to be the most reliable misspecified distribution in terms of lowest BIAS and RRMSE values and lack of sensitivity to the value of the shape parameter. For the case where the 2- or 3-parameter Weibull distribution is true, the most reliable misspecified distribution is the 2-parameter gamma distribution. The 3-parameter gamma and Weibull distributions are the most reliable misspecified distributions when the 2- or 3-parameter lognormal distribution is true.

Keywords:

• Gamma distribution
• lognormal distribution
• weibull distribution
• location parameter
• scale parameter
• shape parameter
• maximum likelihood
• mmisspecified non-nested models
• performance criteria

^* The authors wish to thank an anonymous referee for helpful comments. The third author wishes to acknowledge the financial support of the Australian Research Council

^* The authors wish to thank an anonymous referee for helpful comments. The third author wishes to acknowledge the financial support of the Australian Research Council

Notes

^* The authors wish to thank an anonymous referee for helpful comments. The third author wishes to acknowledge the financial support of the Australian Research Council