Motivated by applications in Bayesian analysis we introduce a multidimensional beta distribution in an ordered simplex. We study properties of this distribution and connect them with the generalized incomplete beta function. This function is crucial in applications of multidimensional beta distribution, thus we present two efficient numerical algorithms for computing the generalized incomplete beta function, one based on Taylor series expansion and another based on Chebyshev polynomials.

翻译：受贝叶斯分析中应用需求的启发，我们在有序单纯形上引入了一种多维贝塔分布。我们研究了该分布的性质，并将其与广义不完全贝塔函数联系起来。由于该函数在多维贝塔分布的应用中至关重要，因此我们提出了两种计算广义不完全贝塔函数的高效数值算法：一种基于泰勒级数展开，另一种基于切比雪夫多项式。