Estimation of Hazard Rate Function for Building Second Order Mixed Model Using Fuzzy Techniques

Article type: Research Article

Authors: Hassan, Dhwyia Salman | Hazem Zaki, Azzah^{a; *} | Hawash, Mohammed Kadim^b

Affiliations: Business Information Technology Department, Business Information College, University of Information Technology and Communications, Baghdad, Iraq | [a] Media Technology Engineering Department, Engineering College, University of Information Technology and Communications, Baghdad, Iraq | [b] College of Administration and Economics, Al Farahidi University Iraq, Baghdad

Correspondence: [*] Corresponding Author. [email protected]

Abstract: This research deals with constructing second order mixed model, from Exponential (θ), and Gamma (3,θ), where the mixing proportions are (αα+1),(1α+1). The p.d.f. is derived, and also CDF and reliability function. Then the parameters are estimated by method of moments and maximum likelihood as well as some proposed method. Where from Table 1 we find the first best fuzzy hazard rate is moment estimator with percentage and the second one proposed while the third best one is maximum likelihood estimation. We observe that the first best fuzzy hazard rate estimator is proposed one, and the second best one is maximum likelihood estimation and finally the moment estimator is best, according to the results of fuzzy hazard rate function, we find that the first best is the proposed one, while the second best one is moments estimator, and finally the third one is maximum likelihood estimation. All the derivation required are explained, and results of comparison are explained in tables.

Keywords: Maximum likelihood estimation, moment estimation, proposed method estimation, second order mixed model

DOI: 10.3233/AJW220030

Journal: Asian Journal of Water, Environment and Pollution, vol. 19, no. 2, pp. 109-116, 2022