TY - JOUR
T1 - Further properties and new applications of the nested Dirichlet distribution
AU - Tian, Guo Liang
AU - TANG, Man Lai
AU - Yuen, Kam Chuen
AU - Ng, Kai Wang
N1 - The research of ML Tang was fully supported by a grant (HKBU261007) from the Research Grant Council of the Hong Kong Special Administrative Region.
PY - 2010/2/1
Y1 - 2010/2/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=70350571187&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2009.08.022
DO - 10.1016/j.csda.2009.08.022
M3 - Journal article
AN - SCOPUS:70350571187
SN - 0167-9473
VL - 54
SP - 394
EP - 405
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
IS - 2
ER -
