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.
