The odd log-logistic Lindley-G family of distributions: properties, Bayesian and non-Bayesian estimation with applications

• Published in: Computational statistics Vol. 35; no. 1; pp. 281 - 308
• Main Authors: Alizadeh, Morad, Afify, Ahmed Z., Eliwa, M. S., Ali, Sajid
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2020; Springer Nature B.V
• Subjects: Bayesian analysis; Computer simulation; Economic Theory/Quantitative Economics/Mathematical Methods; Estimating techniques; Mathematics and Statistics; Maximum likelihood estimates; Maximum likelihood estimators; Monte Carlo simulation; Original Paper; Parameter estimation; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistics; Hazard rate function; Lindley distribution; Bayesian estimation; Maximum likelihood; Simulation
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-019-00932-9

In this paper, a new class of distributions called the odd log-logistic Lindley-G family is proposed. Several of its statistical and reliability properties are studied in-detail. One members of the proposed family can have symmetrical, right-skewed, leftt-skewed and reversed-J shaped densities, and decreasing, increasing, bathtub, unimodal and reversed-J shaped hazard rates. The model parameters are estimated using the maximum likelihood and Bayesian methods. Monte-Carlo simulation study is carried out to examine the bias and mean square error of maximum likelihood and Bayesian estimators. Finally, four real data sets are analyzed to show the flexibility of the new family.