In Bayesian analysis, the well-known beta–binomial model is largely used as a conjugate structure, and the beta prior distribution is a natural choice to model parameters defined in the (0,1) range. The Kumaraswamy distribution has been used as a natural alternative to the beta distribution and has received great attention in statistics in the past few years, mainly due to the simplicity and the great variety of forms it can assume. However, the binomial–Kumaraswamy model is not conjugate, which may limit its use in situations where conjugacy is desired. This work provides the exact posterior distribution for the binomial–Kumaraswamy model using special functions. Besides the exact forms of the posterior moments, the predictive and the cumulative posterior distributions are provided. An example is used to illustrate the theory, in which the exact computation and the MCMC method are compared.

在贝叶斯分析中，众所周知的β-二项式模型主要用作共轭结构，β先验分布是对（0,1）范围内定义的参数进行建模的自然选择。Kumaraswamy分布已被用作Beta分布的自然替代方法，并且由于其简单性和可采用的多种形式，在过去的几年中受到了统计学的高度关注。但是，二项式-Kumaraswamy模型不是共轭的，这可能会限制需要共轭的情况的使用。这项工作使用特殊功能为二项式-Kumaraswamy模型提供了精确的后验分布。除了后矩的确切形式外，还提供了预测性和累积性的后验分布。举一个例子来说明这个理论，