Computation of Maximum-Likelihood Parameters of the Generalized Logistic Distribution by Three-Step Newton–Raphson Algorithm

Açanal Haktanır N., Haktanir T.

Journal of Statistical Theory and Practice, vol.16, no.3, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1007/s42519-022-00243-1
  • Journal Name: Journal of Statistical Theory and Practice
  • Keywords: Parameters of the generalized logistic distribution by the methods of moments, Probability-weighted moments, Maximum-likelihood
  • Erciyes University Affiliated: Yes

Abstract

© 2022, Grace Scientific Publishing.The skewness coefficient (G) of the generalized logistic (GLO) distribution is a function of its shape parameter (a) only. Both the methods of probability-weighted moments and maximum-likelihood (ML) mostly yield magnitudes for the shape parameter much different from that by the method of moments, the gap narrowing with increasing length of the sample series. The computation of ML parameters by the conventional Newton–Raphson method is problematic with no solution for a non-negligible number of sample series. Here, the three-step Newton–Raphson algorithm, which was previously proposed for the generalized extreme values distribution, is adapted to the GLO distribution, and on many recorded annual flood peaks and annual maximum rainfalls series and through a comprehensive Monte-Carlo experiment it is shown to improve the rate of convergent solutions considerably.