The Odd Lindley-G Family of Distributions

We propose a new generator of continuous distributions with one extra positive parameter called the odd Lindley-G family. Some special cases are presented. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Various structural properties of the new family, which hold for any baseline model, are derived including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, Renyi entropy, reliability, order statistics and their moments and k upper record values. We provide a Monte Carlo simulation study to evaluate the maximum likelihood estimates. We discuss estimation of the model parameters by maximum likelihood and provide an application to a real data set.