International Journal of Industrial Engineering & Production Research

The Weibull distribution has been widely used in survival and engineering reliability analysis. In life testing experiments is fairly common practice to terminate the experiment before all the items have failed, that means the data are censored. Thus, the main objective of this paper is to estimate the reliability function of the Weibull distribution with uncensored and censored data by using Bayesian estimation. Usually it is assigned prior distributions for the parameters (shape and scale) of the Weibull distribution. Instead, we assign prior distributions for the reliability function for a fixed time, that is, for the parameter of interest. For this, we propose different non-informative prior distributions for the reliability function and select the one that provides more accurate estimates. Some examples are introduced to illustrate the methodology and mainly to investigate the performance of the prior distributions proposed in the paper. The Bayesian analysis is conducted based on Markov Chain Monte Carlo (MCMC) methods to generate samples from the posterior distributions

Empirical studies show that there is stronger dependency between large losses than large profit in financial market, which undermine the performance of using symmetric distribution for modeling these asymmetric. That is why the assuming normal joint distribution of returns is not suitable because of considering the linier dependence, and can be lead to inappropriate estimate of VaR. Copula theory is basic tool for multivariate modeling, which is defined by using marginal and dependencies between variables joint distribution function. In addition, Copulas are able to explain and describe of complex multiple dependencies structures such as non-linear dependence. Therefore, in this study, by combining symmetric and asymmetric GARCH model for modeling the marginal distribution of variables and Copula functions for modeling financial data and also use of DCC model to determine the dynamic correlation structure between assets, try to estimate the Value at Risk of investment portfolio consists of five active index In Tehran Stock Exchange. The results demonstrate excellence of GJR-GARCH(1,1) with the distribution of t-student for marginal distribution. t-Copula model, estimates the Value at Risk model less than the Gaussian Copula in all cases.