Inverse power XLindley distribution with statistical inference and applications to engineering data.

In this article, a new two-parameter distribution is constructed using the inverse transformation technique on the power XLindley distribution. It is called the inverse power XLindley distribution. As an attractive property, it can generate symmetric and asymmetric probability density functions, ideal for modeling lifetime phenomena. In addition, it is suitable for various real data since the corresponding hazard rate function has an increasing, decreasing, reverse J-shape or J-shape. Essential characteristics and features of our study include quantiles, moments, inverse moments, probability-weighted moments, incomplete moments, and inequality measures. The inferences from the distribution are explored. In particular, the parameters are determined using twelve efficient estimation methods. These methods are maximum likelihood, Anderson-Darling, right-tailed Anderson-Darling, left-tailed Anderson-Darling, Cramér-von Mises, least squares, weighted least squares, maximum product of spacing, minimum spacing absolute distance, minimum spacing absolute-log distance, percentiles, and Kolmogorov. The performance of the resulting estimates is analyzed using Monte Carlo simulation. The numerical results and graphical presentation indicate that the maximum product of spacing estimation approach has the highest accuracy and precision. Using three real data sets and comparisons with other distributions, the effectiveness of the proposed distribution is demonstrated and visually presented.