Work

Mis-specification effects on mean and model choice: A comparison of log-normal and log-logistic distributions

Year: 2026

Type: article

Abstract: The log-normal and log-logistic distributions are frequently used to model positively skewed data. Despite the availability of numerous model selection techniques, the risk of mis-specification between these two closely related models remains substantial. An incorrect model choice can distort the estimation of key statistical measures. This study investigates how model mis-specification affects mean estimation under mis-specification. We derive the maximum likelihood estimator (MLE) and quasi-MLE (QMLE) of the log-normal mean under a mis-specified log-logistic model and vice versa. We construct bootstrap confidence intervals for both MLE and QMLE to evaluate estimation uncertainty under model mis-specification. Analytical expressions for the ratio of biases and the ratio of mean squared errors are used to quantify the distortion introduced by mis-specification. Simulation and bootstrap experiments validate the theoretical findings and demonstrate the practical implications. A real-world dataset is also analysed to illustrate the applicability of the proposed model selection strategy.

Source: Ain Shams Engineering Journal

DOI: 10.1016/j.asej.2026.104226

Authors: Ramendra Yadav, Ravinder Singh, Bishal Diyali, Abdullah Mohammed Alomair

Institutions: Central University of Haryana, Presidency University, King Faisal University

Language: English

Topic: Statistical Distribution Estimation and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funders: Deanship of Scientific Research, King Khalid University, Council for Scientific and Industrial Research, South Africa, University Grants Commission, King Faisal University