Lindley–exponential slash distribution

Abstract

There is a problem arising when Lindley distribution is used to model right–skewed and unimodal data, which lies in its inability to model data with its peak farther from 0. A modification is required to increase the flexibility of this distribution, with “transformed–transformer” being one of the proposed method. This method is done by making a composition of two random variables through their respective distribution functions, with random variable T being the “transformed”, and random variable X being the “transformer”. In this paper, Lindley distribution was chosen to be the “transformed” and exponential distribution was chosen to be the “transformer”, constructing the Lindley–exponential distribution. However, there is a trouble using distribution if the data has a heavier tail. An alternative distribution is required while maintaining the properties of the Lindley-Exponential Distribution. Through transformation of variables method, a new distribution, Lindley-Exponential Slash Distribution is introduced, which is unimodal, right–skewed, heavier tailed. This paper covered some of its statistical characteristics, such as pdf, cdf, survival function, hazard rate, k th moment, mean, variance, skewness, and kurtosis. Parameter estimation was carried out with maximum likelihood estimation through numerical method. An application of distribution was illustrated on maximum annual precipitation data of Durham City.