Two-Parameter Logistic-Exponential Distribution: Some New Properties and Estimation Methods

Abstract

The logistic exponential (LE) distribution is the only two parameter distribution that exhibits five hazard rate shapes such as constant, increasing, decreasing, bathtub, and upside-down bathtub. Due to its practical utility, this article considers ten frequentist methods of estimation, namely, maximum likelihood, least square, weighted least square, percentiles, maximum and minimum spacing distance, and variant of the method of the minimum distances for the LE parameters. A Monte Carlo simulation study is carried out to compare the performance of these estimation methods. Furthermore, Bayesian estimation under the squared error loss function assuming gamma priors for both parameters of the LE distribution is also discussed. The posterior summaries are obtained by using a Markov chain Monte Carlo algorithm. To show the practical superiority, a real-life data is analyzed to show that the LE model performs better than the well-known two-parameter models, like, exponentiated-exponential, Nadarajah–Haghighi, Birnbaum–Saunders, Weibull, Gamma, inverse Gaussian, and log-normal.

KEY WORDS AND PHRASES:

• Bayes estimator
• highest posterior density intervals
• importance sampling
• logistic distribution
• maximum likelihood estimator
• percentile estimator

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05
• 62N05
• 62F102

Acknowledgments

The authors would like to express their gratitude to anonymous referee and the editor for their constructive comments.