论文标题
广义分数分布：β-二项式分布的分散延续
Generalised Score Distribution: Underdispersed Continuation of the Beta-Binomial Distribution
论文作者
论文摘要
一类离散概率分布包含具有有限支持的分布。一个典型的示例是李克特量表的一些变体，响应映射到$ \ {1，2，\ ldots，5 \} $或$ \ { - 3，-2，-2，\ ldots，2，3 \} $ set。具有有限支持的离散分布的一个有趣的子类限于两个参数，并且概率单调性的变化不超过一个。本文的主要贡献是提出适合上述描述的分布家族，我们称之为广义分数分布（GSD）类。提议的GSD类涵盖了所有固定和有限支持的可能的均值和差异集。此外，GSD类可被视为重新配合β-二项式分布的延伸不足的延续。 GSD类参数是直观的，可以通过矩方法轻松估算。我们还为GSD类提供了最大似然估计（MLE）算法，并证明该类正确描述了来自24个多媒体质量评估实验的响应分布。最后，我们表明，GSD类可以表示为二分法零一个随机变量的总和，该变量指出了对类的有趣解释。
A class of discrete probability distributions contains distributions with limited support. A typical example is some variant of a Likert scale, with response mapped to either the $\{1, 2, \ldots, 5\}$ or $\{-3, -2, \ldots, 2, 3\}$ set. An interesting subclass of discrete distributions with finite support are distributions limited to two parameters and having no more than one change in probability monotonicity. The main contribution of this paper is to propose a family of distributions fitting the above description, which we call the Generalised Score Distribution (GSD) class. The proposed GSD class covers the whole set of possible mean and variances, for any fixed and finite support. Furthermore, the GSD class can be treated as an underdispersed continuation of a reparametrized beta-binomial distribution. The GSD class parameters are intuitive and can be easily estimated by the method of moments. We also offer a Maximum Likelihood Estimation (MLE) algorithm for the GSD class and evidence that the class properly describes response distributions coming from 24 Multimedia Quality Assessment experiments. At last, we show that the GSD class can be represented as a sum of dichotomous zero-one random variables, which points to an interesting interpretation of the class.
