Transmuted distributions are skewed family of distributions and used to model and analyze reliability data. In this article, Bayesian estimation of the two-component mixture of transmuted Fréchet distribution assuming type-I right censored sampling scheme is discussed. In order to estimate the unknown parameters, we consider non-informative and informative priors under squared error loss function, precautionary loss function and quadratic loss function, respectively. Furthermore, Bayesian credible intervals of the model are also discussed. Since the posterior distribution is not in close form, we present a Markov Chain Monte Carlo (MCMC) algorithm to obtain different posterior summaries, including Bayes estimates, posterior risks and credible intervals. The performance of Bayes estimators under different loss functions has been compared in terms of their respective posterior risks by analyzing the simulated and real-life data sets in terms of different sample sizes and censoring rates. Two reliability data sets are also analyzed in this study. Significance In life testing experiments, including prior information related to the phenomenon under investigation helps us in making prediction. To save time and cost, we have utilized the concept of type-I censoring and derived the Bayes estimators and posterior risks of the mixture of Transmuted Fréchet distribution. Using simulated and reliability data sets, a comparison assuming different types of priors and loss functions is also given in this study. The choice of transmuted distribution is done on the basis of its flexibility to model skewed data. To compute the Bayes estimates, we have used a MCMC technique.

变态分布是偏态分布族，用于建模和分析可靠性数据。在本文中，讨论了假设I型右删失采样方案的变迁Fréchet分布的两成分混合的贝叶斯估计。为了估计未知参数，我们分别考虑平方误差损失函数，预防损失函数和二次损失函数下的非信息先验和信息先验。此外，还讨论了模型的贝叶斯可信区间。由于后验分布不是紧密的形式，因此我们提出了一种马尔可夫链蒙特卡洛（MCMC）算法来获得不同的后验总结，包括贝叶斯估计，后验风险和可信区间。通过分析不同样本量和审查率下的模拟数据和实际数据集，比较了贝叶斯估计器在不同损失函数下的性能，并根据它们各自的后验风险进行了比较。本研究还分析了两个可靠性数据集。意义在生命测试实验中，包括与被调查现象有关的先验信息，有助于我们进行预测。为了节省时间和成本，我们采用了I型审查的概念，并推导了变换Fréchet分布混合的贝叶斯估计量和后验风险。使用模拟和可靠性数据集，在这项研究中还给出了假设不同类型的先验和损失函数的比较。mut变分布的选择是基于其对偏斜数据进行建模的灵活性。为了计算贝叶斯估计，我们使用了MCMC技术。