Abstract
This paper interested to Bayesian estimation of Weibull distribution parameters under Non-Linear exponential Loss function which proposed by Saiful Islam,Roy and Ali,2004 in the state of informative (Conjugate Prior) when the shape parameter is known and two parameters are unknown with determine optimal sample size from two cases, where the generation of the random data using the simulation for estimate Weibull distribution parameters in first case under the same distribution from different sample sizes (n=10,50,100) and (N=1000), taking initial values for the parameters and initial value b, in addition to taking real data that follow this distribution, to get to estimator balancedadd between two loss function with determine optimal sample size.
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