One-parameter linear-exponential distribution

Abstract

In this paper, we introduce a new continuous probability distribution which is based on the product of linear and exponential functions having a single parameter and hence, we named it ‘One-parameter Linear-exponential distribution’. Different structural properties such as probability density function, probability distribution function and moment generating function of this distribution have been derived. Moments about origin and hence, the first four central moments of the proposed distribution have been obtained. The hazard rate function and the mean residual life function of the proposed distribution have been discussed, and show its flexibility over Lindley distribution. Estimation of parameters has been discussed by the method of moments as well as the method of maximum likelihood. Goodness of fit has been applied to different data-sets which were used by others. It has been observed that the proposed distribution gives better fit to the most of data-sets of same nature, having variance greater than the mean, than Lindley distribution.