Abstarct
In this study, we used Bayesian method to estimate scale parameter for the Nakagami distribution. By considering several of double prior distributions for the scale parameter of the Nakagami distribution ,it means we have two different information about the prior distributions , such as inverted exponential- levy distribution and inverted exponential -gumbel type-II distribution and levy - gumbel type-II distribution and Inverted exponential -non- informative distribution and levy- Non- informative distribution and gumbel type-II - non- informative distribution.We derived the posterior distribution for the scale parameter of the Nakagami distribution according to each of double prior distributions. Also, we derived bayes estimators for the scale parameter of the Nakagami distribution based on squared error loss function. we used simulation technique to compare between these estimators. Several cases from Nakagami distribution for data generating, or different sample sizes (small, medium, and large),by programs written using MATLAB-R2017b program.Simulation results shown that the best estimation for the scale parameter for the Nakagami distribution according to the smallest value of MSE all sample sizes, when the double prior distribution is gumbel type-II- Non- Informative distribution with the parameters for and and .Also, when the double prior distribution is inverted exponential -gumbel type-II distribution with the parameters for .Also, when the double prior distribution is levy- non- informative distribution with the parameters for .Also, when the double prior distribution is inverted exponential- levy distribution with the parameters with .
