Abstract
In this paper, estimation the parameters of Modified Weibull Extension Distribution by using maximum likelihood estimator method, by utilizing Monte Carlo method in simulation procedure for generate many various of samples sizes with many various of replicate the sample size. Subsequently finding the estimate of the Survival function. Then fuzzify the estimation of the parameters for the same various of samples sizes with same various of replicate the sample size which obtained from Monte Carlo method in simulation procedure, by using Linear Symmetric Pentagonal Fuzzy Numbers, and propose Non - Linear Symmetric Pentagonal Fuzzy Numbers which came from expanding the new propose method of interval estimation to five fuzzy numbers membership for the parameters of Modified Weibull Extension Distribution for all the same various of samples sizes with same various of replicate the sample size. Then, transform all the fuzzy parameters to crisp parameters using propose Ranking functions with Linear Symmetric Pentagonal Fuzzy Numbers, and propose Non - Linear Symmetric Pentagonal Fuzzy Numbers. Consequently finding the Survival function. The outcome of Survival functions before and after fuzzy work will be compared using mean square error.
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