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In this paper ,we study estimation of two parameters of Weibull distribution .Methods of estimation used are maximum likelihood estimator (MLE) and Bayes. We compared the numerical results by simulation in MATLAB program. The comparison show that the Bayes estimator gives the best results ( less error) .

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The concept of length biased distribution can be used for analyzing life time data, which need adjusting the original probability distribution, here we consider two of size biased distributions, which are [ size – biased Poisson distribution (SBPD)] and second is [ size – biased generalized discrete logarithmic distribution (SBLSD)]. For the first, the scale parameter (

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The aim of this paper to find Bayes estimator under new loss function assemble between symmetric and asymmetric loss functions, namely, proposed entropy loss function, where this function that merge between entropy loss function and the squared Log error Loss function, which is quite asymmetric in nature. then comparison a the Bayes estimators of exponential distribution under the proposed function, whoever, loss functions ingredient for the proposed function the using a standard mean square error (MSE) and Bias quantity (Mbias), where the generation of the random data using the simulation for estimate exponential distribution parameters different sample sizes (n=10,50,100) and (N=1000), taking initial values for the parameters and initial value b, to get to estimator balanced add between two loss function ,moreover, the optimal sample size determination under proposed entropy loss function.

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