In this paper, we developed linear exponential (LINEX) loss function by emerging weights to produce weighted linear exponential (WLINEX) loss function. Then we utilized WLINEX to derive scale parameter and reliability function of the Weibull distribution based on record values when the shape parameter is known. After, we estimated scale parameter and reliability function of Weibull distribution by using maximum likelihood (ML) estimation and by several Bayes estimations.  The Bayes estimates were obtained with respect to symmetric loss function (squared error loss (SEL)), asymmetric loss function (LINEX) and asymmetric loss function (WLINEX). The ML and the different Bayes estimates are compared via a Monte Carlo simulation study. The result of simulation mentioned that the proposed WLINEX loss function is promising and can be used in real environment especially at the case of underestimate where it revealed better performance than LINEX loss function for estimating scale parameter.

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<abstract> <p>It is known in the financial world that the index price reveals the performance of economic progress and financial stability. Therefore, the future direction of index prices is a priority of investors. This empirical study investigated the effect of incorporating memory and stochastic volatility into geometric Brownian motion (GBM) by forecasting the future index price of S&amp;P 500. To conduct this investigation, a comparison study was implemented between twelve models; six models without memory (GBM) and six models with memory (GFBM) under two different assumptions of volatility; constant, which were computed by three methods, and stochastic volatility, obeying three deterministic functions. The results showed that the best performance model was for GFBM under a stochastic volatility assumption using the identity deterministic function $ \sigma \left({Y}_{t}\right) = {Y}_{t} $, according to the smallest values of mean square error (MSE) and mean average percentage error (MAPE). This revealed the direct positive effect of incorporating memory and stochastic volatility into GBM to forecast index prices, and thus can be applied in a real financial environment. Furthermore, the findings showed invalidity of the models with exponential deterministic function $ \sigma \left({Y}_{t}\right) = {e}^{{Y}_{t}} $ in forecasting index prices according to huge values of MAPE and MSE.</p> </abstract>