Properties and Applications of the Type I Half-logistic Nadarajah-Haghighi Distribution

Abstract

A new three-parameter distribution called the type I half-logistic Nadarajah-Haghighi (T IHL N H ) is proposed. We discussed some important mathematical and statistical properties of the new model such as an explicit form of its r th moment, mean deviations,
quantile function, Bonferroni and Lorenz curves. The Shannon entropy and Renyi entropy are computed, the expression for the Kullback-Leibler divergence measure is provided. The model parameters estimation was approached by the maximum likelihood
estimation (MLE), and the information matrix is obtained. The finite sample properties of the MLEs are investigated numerically by simulation studies; by examining the bias and mean square error of the estimators, and the results was satisfactory. We used two
real data applications to demonstrate the superior performance of the T IHL N H in terms of fit over some other existing lifetime models.