A Penalized Maximum Likelihood Estimation for the Log-Logistic Distribution with Complete Data

Title

A Penalized Maximum Likelihood Estimation for the Log-Logistic Distribution with Complete Data

Creator

Anupama, S.; Azarudheen, S.; Gogi, Vyshali J.

Description

Penalized maximum likelihood estimation is specified for estimating parameters of a log-logistic distribution for complete-data situations. This approach addresses the issues of Maximum Likelihood Estimation, wherein Maximum Likelihood Estimation is often unstable when sample sizes are small, and fails with heavy-tailed or asymmetric data. By adding a ridge penalty to the log-likelihood, we derive new score equations, which are solved numerically. The performance is measured for a variety of shape and scale parameters and sample sizes, with bias and Mean Squared Error as the two main measures. The simulation experiment results indicate Penalized maximum likelihood estimation consistently achieves lower bias and Mean Square Error with small sample sizes and particularly strong improvements under skewed or heavy-tailed data. With larger sample size, the differences between Maximum Likelihood Estimation and Penalized maximum likelihood estimation decrease, as we would expect. These results suggest that Penalized maximum likelihood estimation is a viable estimation method using the log-logistic distribution, especially with small or limited datasets. The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2026.

Source

Communications in Computer and Information Science;Volume;2853 CCIS;pp.313-323

Date

01-01-2026

Publisher

Springer Science and Business Media Deutschland GmbH

Subject

log-logistic distribution; parameter estimation; penalized maximum likelihood estimation; ridge penalty; simulation study

Coverage

Anupama S., Department of Data Science and Statistics, CHRIST University, Bengaluru, India; Azarudheen S., Department of Data Science and Statistics, CHRIST University, Bengaluru, India; Gogi V.J., Department of Data Science and Statistics, CHRIST University, Bengaluru, India

Rights

Restricted Access; Hardcopy may be available in the library

Relation

ISSN: 18650929; ISBN: 978-981957291-5;

Format

online

Language

English

Type

Conference paper

Identifier

https://doi.org/10.1007/978-981-95-7292-2_24

https://www.scopus.com/pages/publications/105038784152?origin=resultslist