Univariate and Bivariate Discrete Nadarajah and Haghighi Distributions

Abstract

Exponential distribution is one of the most familiar lifetime distribution used to model observed failures of different types of phenomena and components. A new extension of Weibull distribution known as the Nadarajah and Haghighi was introduced in litrature to accomolate the inflation in data. However in practice, discrete data is easy to collect as compared to continuous data. Thus keeping in mind the utility of discrete data, this thesis focus on the developement of new discrete probability distribution model. First, we proposed a univariate discrete Nadarajah and Haghihgi distribution by using the Marshal-Olkin method. We derived the mathematical and statistical properties of the proposed univariate discrete Nadarajah and Haghighi distribution. To assess the performance of different estimation methods, we considered, e.g, Maximum likelihood method, the method of least and weighted least squares, Percentile estimation method, Maximum product spacing, Cramer Von-Mises, Anderson Darling and right Anderson Darling method. To show application of the proposed distribution, two real data sets are used. Next, we proposed the bivariate discrete Nadarajah and Haghighi distribution (BNDH) by using the maximum-minimum method of the univariate discrete Nadarajah and Haghighi distribution. We discussed different properties of the proposed bivariate discrete N adarajah and Haghighi distribution. The performance of the proposed model has been evaluateed uses the aforementioned methods of estimation. To show real life application, we used two different data sets to evaluate the performance of the proposed model and compare this newly model with the existing bivariate discrete generalized exponential distribution (BDGE) and bivariate discrete Wei bull distribution (BDvV).