Inverse Lindley distribution: different methods for estimating their PDF and CDF

Abstract

The probability density and cumulative distribution functions are essential statistical forms in modelling data and characterizing their respective distributions. This study addresses the estimation problem of these basic functions for the inverse Lindley distribution. The maximum likelihood, uniformly minimum variance unbiased and Bayes estimators are considered here. The exact confidence intervals for the probability density and cumulative distribution functions of the inverse Lindley distribution are also derived. A real data application and simulation studies are performed for illustrating and comparing among the so developed methods.

Keywords:

• Inverse Lindley distribution
• maximum likelihood estimator
• uniformly minimum variance unbiased estimator
• confidence interval
• Bayesian estimation
• importance sampling

Disclosure statement

No potential conflict of interest was reported by the author(s).