Alpha Power Transformed Extended Inverse Lindley Distribution: Properties and its Applications

Abstract

Variable transformation is a fundamental concept in probability and distribution theory and has been widely employed to enhance the flexibility of statistical models. The alpha power transformation (APT) is a useful technique for extending existing distributions to provide better fits to real-life data. In this article, we introduce a new four-parameter distribution, termed the alpha power transformed extended inverse Lindley distribution (APTEILD). Several distributional and statistical properties of the proposed model are derived, including the probability density function, cumulative distribution function, hazard rate function, moment generating function, quantile function, median, mode, order statistics, and entropy measures. Parameter estimation is carried out using five estimation methods: maximum likelihood estimation, maximum product spacing, ordinary least squares, weighted least squares, and the Cramér–von Mises approach. A Monte Carlo simulation study is conducted to generate random samples from the proposed distribution and to examine the finite-sample performance of the estimators. The practical applicability of the APTEILD model is illustrated using three real-life datasets. In addition, likelihood ratio tests are performed to assess the adequacy of the proposed model in comparison with its nested counterparts.