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In many applications, observations have a skewness, an elongated shape, a heavy tail, a multi-mode structure, or a mixed distribution. Therefore, models based on the normal distribution cannot provide correct inferences under such conditions and can lead to biased estimators or increased variance. The Laplace distribution and its generalizations can be suitable alternatives in such situations due to their elongation, heavy tails, and skewness. On the other hand, in models based on mixed distributions, there is always a possibility that fewer samples are available from one or more components. Therefore, given the Bayesian approach's advantage in handling small samples, this research developed a Bayesian model to fit a finite mixed regression model with skew-Laplace distributions and conducted a simulation study to assess its performance. Laplace has been compared in two approaches, frequentist and Bayesian. The results show that the Bayesian approach of the model is more effective than other  models.

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In this paper, estimation and prediction for the size-biased exponential distribution are studied based on upper records. Both estimation and prediction for future records are performed within classical and Bayesian frameworks. Maximum likelihood estimation, method of moments estimation, and Bayesian estimation for the parameter of the size-biased exponential distribution are obtained based on the symmetric squared error loss function. Since the integrals associated with the Bayesian estimators and predictors do not have closed-form solutions, Lindley's approximation method, the importance sampling method, and the  MCMC method are used to approximate them. Asymptotic, pivotal, maximum likelihood, and Bayesian confidence intervals are constructed. Furthermore, prediction intervals for future records are investigated. A Monte Carlo simulation study is conducted to evaluate and compare the performance of the different estimation and prediction methods. Finally, a real-world example is provided to illustrate the proposed methodology.