Estimating the percentiles of some misspecified non-nested distributions*

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 ...