A generalization of generalized beta distributions

A generalization of generalized beta distributions
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广义贝塔分布的推广

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发表时间：
1998
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通讯作者：
Michael B. Gordy
Michael B. Gordy
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文献类型：
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作者：
Michael B. Gordy

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介绍了“复合合流超几何”(CCH)分布。CCH统一和推广了最近引入的贝塔分布的三个推广：Armero和Bayarri(1994)的Gauss超几何(GH)分布，McDonald和Xu(1995)的广义贝塔(GB)分布，以及Gordy(即将到来)的合流超几何(CH)分布。与测试版、GB版和GH版不同，CCH允许以一种自然和方便的方式对解释变量进行条件作用。CCH系列是伽马分布信号的共轭，因此在贝叶斯分析中也可能被证明是有用的。通过两个衡量家庭流动资产的指标对CCH的应用进行了论证。在每种情况下，CCH在匹配方面都比限制性更强的替代方案产生了统计上的显著改善。
This paper introduces the ``compound confluent hypergeometric' (CCH) distribution. The CCH unifies and generalizes three recently introduced generalizations of the beta distribution: the Gauss hypergeometric (GH) distribution of Armero and Bayarri (1994), the generalized beta (GB) distribution of McDonald and Xu (1995), and the confluent hypergeometric (CH) distribution of Gordy (forthcoming). Unlike the beta, GB and GH, the CCH allows for conditioning on explanatory variables in a natural and convenient way. The CCH family is conjugate for gamma distributed signals, and so may also prove useful in Bayesian analysis. Application of the CCH is demonstrated with two measures of household liquid assets. In each case, the CCH yields a statistically significant improvement in fit over the more restrictive alternatives.