Estimation of asymptotic variances of quantiles for the generalized logistic distribution

Hongjoon Shin, Taesoon Kim, Sooyoung Kim, Jun Haeng Heo

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this study, the parameter estimations for the 3-parameter generalized logistic (GL) distribution are presented based on the methods of moments (MOM), maximum likelihood (ML), and probability weighted moments (PWM). The asymptotic variances of the MOM, ML, and PWM quantile estimators for the GL distribution are expressed as functions of the sample size, return period, and parameters. A Monte Carlo simulation was performed to verify the derived expressions for variances and covariances between parameters and to evaluate the applicability of the derived asymptotic variances of quantiles for the MOM, ML and PWM methods. The simulation results generally show good agreement with the analytical results estimated from the asymptotic variances of parameters and quantiles when the shape parameter (β) of the GL distribution is between -0. 10 and 0. 10 for the MOM method and between -0. 25 and 0. 45 for the ML and PWM methods, respectively. In addition, the actual sample variances and the root mean square error (RMSE) of asymptotic variances of quantiles for various sample sizes, return periods, and shape parameters were presented. In order to evaluate the applicability of the estimation methods to real data and to compare the values of estimated parameter, quantiles, and confidence intervals based on each parameter estimation method, the GL distribution was fitted to the 24-h annual maximum rainfall data at Pohang, Korea.

Original languageEnglish
Pages (from-to)183-197
Number of pages15
JournalStochastic Environmental Research and Risk Assessment
Volume24
Issue number2
DOIs
Publication statusPublished - 2010

All Science Journal Classification (ASJC) codes

  • Environmental Engineering
  • Environmental Chemistry
  • Safety, Risk, Reliability and Quality
  • Water Science and Technology
  • Environmental Science(all)

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