Ratio of Two Independent Lindley Random Variables

Abstract

The distribution of the ratio of two independently distributed Lindley random variables $$X$$ X and $$Y$$ Y , with different parameters, is derived. The associated distributional properties are provided. Furthermore, the proposed ratio distribution is fitted to two applications data (COVID-19 and Bladder Cancer Data), and compared it with some well-known right-skewed variations of Lindley distribution, namely; Lindley distribution, new generalized Lindley distribution, new quasi Lindley distribution and a three parameter Lindley distribution. The numerical result of the study reveals that the proposed distribution of two independent Lindley random variables fits better to the above said data sets than the compared distribution.

A New Distribution for Modeling Data with Increasing Hazard Rate: A Case of COVID-19 Pandemic and Vinyl Chloride Data

“…Ghitany, Atieh, and Nadarajah [8] showed through a numerical example that the hazard function of the Lindley distribution does not exhibit a constant hazard rate, indicating its improved flexibility over the exponential distribution. The Lindley distribution has recently received considerable attention as an appropriate model to analyze lifetime data, for instance, in Zakerzadeh and Dolati [9], Mazucheli and Achcar [10], Gupta and Singh [11], Warahena-Liyanage and Pararai [12], Onyekwere and Obulezi [13], and very recently Anabike et al [14], Shakil et al [15], among others. An expanded generalized cosine family of distributions was investigated for use in dependability modeling and modeling the COVID-19 mortality rate with a new flexible modification of the log-logistic distribution by Muse et al [16].…”