This research includes new probability distribution which is named beta inverted Lindley distribution. Some useful functions of the proposed distribution are derived. Important mathematical expansions are investigated. Statistical measures including; quantiles, moments, incomplete moments, Rényi and s entropies are acquired. Extra statistical properties such as mean deviations, central of tendency measures, coefficient of variation, coefficients of skewness and kurtosis are defined. The Bonferroni and Lorenz curves are conducted and the stress- strength reliability is computed. The maximum likelihood method is used to estimate parameters of beta inverted Lindley distribution. The importance and significance of the introduced model are applied through failure times data set.
The main aim behind generalization is to make more flexibility to the distribution so that more data can be analyzed using the new distribution.
The model parameters are estimated using maximum likelihood estimation and simulation study is applied. The importance of the presented distribution is illustrated by using real data set. According to the results; the BIL distribution fits better than BIE and IL distributions to the given data.