# The Weibull Lindley: General family of probability distributions

### Abstract

In this paper, a new family of distributions are introduced based on Weibull Lindley (WL) distribution and arbitrary cumulative distribution function (CDF). This family is called Weibull Lindley general family of distributions (WLGFD). Several properties of WLGFD are derived including the PDF, CDF, hazard rate function, reversed hazard function, odd function, and quartile function. On this approach, we derive two distributions: The Weibull Lindley Uniform distribution (WLUD) and Weibull Lindley Exponential distribution (WLED). The PDF, CDF, moment generating function, hazard rate, reversed hazard function, odd function, quartile function and moments are proved of the WLUD and WLED. An estimation procedure by the method of maximum likelihood and a simulation are studied of WLUD and WLED respectively. finally, we give graph of PDF, CDF, mean squared error and bias at different values of parameters of WLUD and WLED.