University of karbala
Faculty of administration and Economics Department of stastistics

Reliability Estimate of the Inverse Gamma Distribution in the Case of Fuzzy Data
Athesis submitted to
Council of the administration and Economics/Karbala university
As partial fulfilment of the requirements for the degree of master of science in statics
By
Baneen Ahmed Hussain

in this study the fuzzy reliability function was estimated for an inverse gamma distribution in light of the fuzzy data, the fuzzy reliability is the fuzzy probability for the unit remaining in working condition after a period of time t has passed. Therefore, three methods were used to estimate the fuzzy reliability function, which is the maximam likelihood method, the bayes method, and the moment method. The three methods were compared by using the standard statistical mean squares of error MSE and average squares of relative error MAPE by using the Monte Carlo simulation method by generating small data (n=25), medium (n = 0) and large (n = 75,100) And hypothetical values of the parameters (α) and (β), and we concluded by means of the simulation results that the fuzzy reliability estimated by the bayes method at a sample size of 25 is the best in the estimation, followed by the maximam likelihood method, either the moment method. It is not suitable for estimating the fuzzy reliability function of an inverse gamma distribution, and the maximum likelihood method outperforms the bayes and moment methods at large sample sizes.
With regard to the application side, a practical application of a random sample of real data with a size of (50) views of restorative ceramics of the teeth was performed in the Dental Health Center of the Karbala Health Department. Goodness of conformity tests were conducted, and it was found that the real data are appropriate for the distribution of the inverse gamma when estimating by the bayes method, then the maximam likelihood and finally the moment method