The Inverse XLindley Distribution: Properties and Application

Abstract

This work proposes a new extension to the XLindley model called an inverse XLindley distribution (IXLD). Its probability density function and hazard rate function shapes were deduced mathematically. Several statistical properties of the IXLD were derived mathematically. We use ten different approaches to calculate the parameters of the IXLD. The asymptotic behaviour of these estimators were studied thanks to a comprehensive simulation investigation. Through modelling real data sets, the effectiveness and applicability of the IXLD are examined. This proves that the IXLD better fits the real data set than competing models.

Keywords

• Lindley distribution
• stress-strength
• Anderson-Darling estimation
• engineering data
• maximum likelihood estimation
• maximum product of spacing