Constructing A New Probability Distribution (Gompertz-Lindely) to Estimate the Reliability Function and the Risk Function

Abstract

In this paper, a new elastic probability distribution was formed by Gompertz-Lindley, a distribution resulting from the combination of the two continuous distributions, Gompretz and Lindley, as measurement parameters for the Gompertz distribution. A random variable then follows the Lindley distribution to produce the probability distribution. Gombertz–Lindley probability distribution is the result of a random variable that follows the Lindley distribution for the Gompertz distribution. The statistical and structural properties of the distribution and the shapes taken by the curves of the probability density function and the risk function were derived, as well as their parameters, which were estimated using the Maximum Likelihood Method. Applying it to a sample of real data represented by continuous survival periods until death served to show how effective distribution is at representing a sample of data. Compared to several traditional distributions, it has been demonstrated that the Gompertz-Lindley distribution fits the data the best.