论文标题
学生t分布的一种新的渐近表示和反转方法
A new asymptotic representation and inversion method for the Student's t distribution
论文作者
论文摘要
一些特殊功能在应用概率和统计数据中特别重要。例如，不完整的beta函数是累积的中央β分布。在本文中，我们考虑了中央学生的 - $ t $分布的反转，这是中央beta分布的一个特殊情况。该分布函数的反转对于假设检验以及根据相应概率密度函数分布的随机样品有用。从互补误差函数方面，新的渐近表示将是我们分析中的重要成分之一。正如我们将显示的那样，这种渐近表示也可用于分布函数的计算。我们说明了所有获得数值示例的近似值的性能。
Some special functions are particularly relevant in applied probability and statistics. For example, the incomplete beta function is the cumulative central beta distribution. In this paper, we consider the inversion of the central Student's-$t$ distribution which is a particular case of the central beta distribution. The inversion of this distribution functions is useful in hypothesis testing as well as for generating random samples distributed according to the corresponding probability density function. A new asymptotic representation in terms of the complementary error function, will be one of the important ingredients in our analysis. As we will show, this asymptotic representation is also useful in the computation of the distribution function. We illustrate the performance of all the obtained approximations with numerical examples.
