Further properties and new applications of the nested Dirichlet distribution

Authors:
Guo-Liang Tian;Man-Lai Tang;Kam Chuen Yuen;Kai Wang Ng
Affiliations:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China;Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China;Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China
Venue:
Computational Statistics & Data Analysis
Year:
2010

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Abstract

Recently, Ng et al. (2009) studied a new family of distributions, namely the nested Dirichlet distributions. This family includes the traditional Dirichlet distribution as a special member and can be adopted to analyze incomplete categorical data. However, other important aspects of the family, such as marginal and conditional distributions and related properties are not yet available in the literature. Moreover, diverse applications of the family to the real world need to be further explored. In this paper, we first obtain the marginal and conditional distributions and other related properties of the nested Dirichlet distribution. We then present new applications of the family in fitting competing-risks model, analyzing incomplete categorical data and evaluating cancer diagnosis tests. Three real data involving failure times of radio transmitter receivers, attitude toward the death penalty and ultrasound ratings for breast cancer metastasis are provided.