###### Abstract  
In this article, a new modification of the Weibull model with three parameters, the new exponential Weibull distribution (E-WD), is defined. The new model has many statistical advantages, the heavy-tailed behavior and the regular variation property were offered. Many of the important statistical functions of the modified model are presented in closed forms. The flexibility of E-WD has been improved. The proposed model can be used to fit data with different shapes, it can be right-skewed, left-skewed, decreasing, curved and symmetric. Some distribution properties of the proposed model, including moment generating function, characteristic function, moment, quantile and identifiability property, have been derived. In addition to the information generating function, the Shannon entropy and information energy are also discussed. The maximum likelihood approach and Bayesian estimation are used to estimate the distribution parameters. In the Bayesian method, three different loss functions are used. The calculations show the biases and estimated risks to obtain the best estimator. The bootstrap confidence intervals, the asymptotic confidence intervals and the observed variance-covariance matrix are obtained. Metropolis Hastings' MCMC procedure is used for the calculations. We apply the composite distribution to stock data for four variables. The goodness-of-fit results show that the model performs well compared to its competitors. The proposed model can be used for forecasting and decision making.  
Weibull distribution; stock market; statistical modeling; bayesian estimation; maximum likelihood estimation +
Footnote †: journal:  
A study on the complex distribution beta-Burr XII was published, in which the characteristics were derived by [PERSON] et al. [5]. A study on the construction of a composite statistical model for the Beta-Half Cauchy distribution was presented by [PERSON] and [PERSON] [6], such as the arithmetic mean and mode, and some properties of the dispersion measures. [PERSON] and [PERSON] [7] published a paper that combined the exponential-Pareto distribution with two independent distributions, the Exponential and the Pareto distribution. The properties of the new distribution were studied in terms of the probability density function, the reliability function, the cumulative function, the risk function, and the use of the method of greatest likelihood to estimate the parameters. [PERSON] and [PERSON] [8] proposed the generalized exponential distribution and [PERSON] [9] estimated the parameters via using different method in person of outlier.  
Many literatures researched the issue of new statistical models based on the Weibull distribution. For example, [PERSON] et al. [10] developed the generalized modified Weibull distribution. [PERSON] et al. [11] developed a beta Weibull model. [PERSON] et al. [12] developed a new Weibull-Pareto distribution. [PERSON] developed the generalised Weibull-Weibull distribution [13]. [PERSON] and [PERSON] [14] developed the generalised Arcsine-Kumaraswamy-X family of distributions by incorporating a trigonometric function, the Weibull claim model [15] using a class of claim distributions, the modified alpha-power Weibull-Weibull model [16], the generalised modified Weibull model [17] and the Khalil generalized Weibull distribution based on ranked set samples [18]. The exponential probability density function is:  
\[f(\chi;\psi)=\psi e^{-\chi\psi},\hskip 28.452756 pt\chi\geq 0,\psi>0. \tag{1}\]  
Here \(\psi>0\) is the inverse scale parameter. The exponential is:  
\[F(\chi;\psi)=1-e^{-\chi\psi},\hskip 28.452756 pt\chi\geq 0,\psi>0. \tag{2}\]  
Next, the Weibull cumulative distribution function with two parameters takes the following form:  
\[G(\chi;\lambda,\theta)=1-e^{-\lambda\chi^{\theta}},\hskip 28.452756 pt\chi\geq 0; \lambda,\theta>0. \tag{3}\]  
where \(\chi\geq 0\), \(\lambda>0\) is the scale parameter and \(\theta>0\) is the shape parameter.