Estimation of the Extreme Value Type I Distribution by the Method of LQ-Moments

Ani Shabri,Abdul Aziz Jemain

doi:10.3844/jmssp.2009.298.304

Abstract

Problem statement: The study evaluated the effectiveness of the various quantile estimators of the LQ-moments method for estimating parameters of the Extreme Value Type 1 (EV1) distribution. Approach: The performances of the LQ-moments were analyzed and compared against a widely used method of L-moments by using simulated samples of both EV1 and generalized Lambda distribution, focusing on small and moderate sample sizes. Results: The analysis results showed that LQMOM method wais more efficient in many cases especially for the upper tails of the distribution and for various sample sizes. Conclusion: This study demonstrated that conventional LMOM was not optimal for the estimation of the EV1 distribution.

Highlights

The Extreme Value Type I (EV1) distribution is widely used in various fields including hydrology for modeling extreme events[5,10,14]
Ani and Jemain[1,2,3] proposed the LQMOM based on the Weighted Kernel Quantile (WKQ) estimator in which the quick estimators parameters α and p are not restricted, such as the median, trimean or Gastwirth on the value of p and α such as the median, trimean or the Gastwirth but we explore an extended class of LQMOM with consideration combinations of p and α values in the range 0 and 0.5
We develop improved the LQMOM that does not impose restrictions on the value of the quick estimators parameters p and a but we explore an extended class of LQ-moments with consideration combinations of p and a values in the range 0 and 0.5

Summary

Introduction

The Extreme Value Type I (EV1) distribution is widely used in various fields including hydrology for modeling extreme events[5,10,14]. The problem is one of selecting an appropriate method for estimating the EV1 distribution parameters. The methods of PWM, ordinary product Moment (MOM) and Maximum Likelihood (ML) estimation are commonly used to estimate the parameter of the EV1 distribution. Landwehr[10] used the method of Probability Weighted Moments (PWM) and the related L-Moments (LMOM). They found that the method, in general, compared with the MLE and MOM methods. Raynal and Salas[14] analyzed six different methods of parameter estimation and preferred PWM for large samples. Phien[12] compared the MOM, ML, ME (maximum entropy) and PWM estimators for the EV1 distribution. PWM estimators were found to be best in terms of mean square error

Objectives

Results

Conclusion