Effects of L-Moments, Maximum Likelihood and Maximum Product of Spacing Estimation Methods in Using Pearson Type-3 Distribution for Modeling Extreme Values

Modeling of extreme values like annual maxima's is important in many applications. Pearson Type-3 (PE3) distribution is an important probability distribution, widely used for modeling of extreme values with a variety of estimation methods. The focus of this study is to assess the effects of three methods of estimation of parameters for PE3 distribution namely L-moments (LM), maximum likelihood estimation (MLE) and maximum product of spacing (MPS). Assessment is based on a two-step approach. The first step uses simulation experiments while the second is based on empirical analyses, by varying size and shape characteristics of the sample. The study concluded that the estimates using LM method have low bias in case of small sample and when data exhibits small to moderate skewness and kurtosis. MPS is a reasonable alternative and provides efficient estimates, especially when the data shows large skewness and kurtosis with small to moderate size of sample. MLE method is useful in case of very large sample size with low values of shape characteristics of data. The results of this study provide useful guidelines for fitting PE3 distribution, especially to extreme values.