A Three Parameter Shifted Exponential Distribution: Properties and Applications

Abstract

This paper proposed a three parameter exponentiated shifted exponential distribution and derived some of its statistical properties including the order statistics and discussed in brief details. Method of maximum likelihood was used to estimate the parameters of the proposed distribution. The proposed distribution was applied on two real life positively skewed data sets with different level of kurtosis and simulation was done. The results obtained indicate that the proposed distribution with unimodal, positively skewed and decreasing shapes property fits better on the data set with higher kurtosis than the data set with lower kurtosis when compared. The simulation results showed that as the sample size increases the biasedness and the mean square error (MSE) of the proposed distribution decreases showing its flexibility property. In both real life applications, the proposed distribution was compared with the three parameter generalized inverted generalized exponential distribution, a three parameter generalized Lindley distribution and the two parameter shifted exponential distribution based on their Alkaike Information Criteria (AIC), Bayesian Information Criteria (BIC), Negative Log-likelihood (NLL) and Hanniquin Information Criteria  (HQIC) values and it indicated that the proposed distribution can be used to model real life situations of positively skewed data with high kurtosis.