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

Abstract

This research deals with constructing second order mixed model, from Exponential (θ), and Gamma (3,θ), where the mixing proportions are $\left(\frac{\alpha }{\alpha +1}\right),\left(\frac{1}{\alpha +1}\right)$.

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.