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Estimation of asymptotic variances of quantiles for the generalized logistic distribution. (English) Zbl 07095981

Summary: 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 (\(\beta\)) 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.

MSC:

62J12 Generalized linear models (logistic models)
62P12 Applications of statistics to environmental and related topics
62J05 Linear regression; mixed models
62F12 Asymptotic properties of parametric estimators
Full Text: DOI

References:

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