Univariate Discrete Nadarajah and Haghighi Distribution: Properties and Different Methods of Estimation

Abstract

An extension of the exponential distribution due toNadarajah and Haghighi referred to as Nadarajah and Haghighi (NH) distribution is an alternative that always provides better fits than the gamma, Weibull, and the generalized exponential distributions whenever the data contains zero values. However, in practice, discrete data is easy to collect as compared to continuous data. Thus, keeping in mind the utility of discrete data, we introduce the discrete analogue of NH distribution. Our main focus is the estimation from the frequentist point of view of the unknown parameters along with deriving some mathematical properties of the new model. We briefly describe different frequentist approaches, namely, maximum likelihood, percentile based, least squares, weighted least squares, maximum product of spacings, Cramèr-von-Mises, Anderson-Darling, and right-tail Anderson-Darling estimators, and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. The potentiality of the distribution is analyzed by means of two real data sets.

Keywords

• maximum likelihood estimator
• least square estimator
• percentile estimator
• anderson darling estimator;
• nadarajah and haghighi distribution