Lambda Upper Bound Distribution: Some Properties and Applications

Abstract

In this work, we proposed a new univariate continuous distribution derived from one-parameter beta distri
bution using the property of probability density function (pdf) and the theory of Riemann integration. The proposed distribution is called Lambda Upper Bound (LUB) Distribution because it is bounded above by Lambda (λ). The proposed distribution with two parameters can also be referred to as two parameter power function distribution and will present new opportunities for assessing reliability and survival data in different field of life such as environmental, engineering, medicine and finance. The distribution was characterized using different functions and different properties of the distribution were derived including the Shannon entropy, order statistics and moment. We used maximum likelihood estimation method to estimate the distribution parameters and they are in closed form. Simulation study was carried out to test the consistency of the parameters estimates and applied two real life data and compared the result with existing distributions. The result of the comparison shows that the proposed distribution, despite having only two parameters fitted well to the two data sets and compared favourably well with other more complex distributions. The proposed distribution is a type of beta distribution with shape and scale parameters and can be used as an alternative to beta, kumaraswamy and uniform distributions.