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Further properties and new applications of the nested Dirichlet distribution

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  • Tian, Guo-Liang
  • Tang, Man-Lai
  • Yuen, Kam Chuen
  • Ng, Kai Wang

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.

Suggested Citation

  • Tian, Guo-Liang & Tang, Man-Lai & Yuen, Kam Chuen & Ng, Kai Wang, 2010. "Further properties and new applications of the nested Dirichlet distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 394-405, February.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:2:p:394-405
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    References listed on IDEAS

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    1. Tang, Man-Lai & Wang Ng, Kai & Tian, Guo-Liang & Tan, Ming, 2007. "On improved EM algorithm and confidence interval construction for incomplete rxc tables," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2919-2933, March.
    2. Rameshwar D. Gupta & Donald St. P. Richards, 2001. "The History of the Dirichlet and Liouville Distributions," International Statistical Review, International Statistical Institute, vol. 69(3), pages 433-446, December.
    3. Fengchun Peng & W.Jack Hall, 1996. "Bayesian Analysis of ROC Curves Using Markov-chain Monte Carlo Methods," Medical Decision Making, , vol. 16(4), pages 404-411, October.
    4. Martin Hellmich & Keith R. Abrams & David R. Jones & Paul C. Lambert, 1998. "A Bayesian Approach to a General Regression Model for ROC Curves," Medical Decision Making, , vol. 18(4), pages 436-443, October.
    5. Ng, Kai Wang & Tang, Man-Lai & Tan, Ming & Tian, Guo-Liang, 2008. "Grouped Dirichlet distribution: A new tool for incomplete categorical data analysis," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 490-509, March.
    6. Gupta, Rameshwar D. & Richards, Donald St. P., 1990. "The Dirichlet distributions and polynomial regression," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 95-102, January.
    7. Gupta, Rameshwar D. & Richards, Donald St.P., 1987. "Multivariate Liouville distributions," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 233-256, December.
    8. Gupta, Rameshwar D. & Richards, Donald St. P., 1992. "Multivariate Liouville distributions, III," Journal of Multivariate Analysis, Elsevier, vol. 43(1), pages 29-57, October.
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    Cited by:

    1. Cheng, Ching-Wei & Hung, Ying-Chao & Balakrishnan, Narayanaswamy, 2014. "Generating beta random numbers and Dirichlet random vectors in R: The package rBeta2009," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1011-1020.
    2. Nguyen, H.D. & Gouno, E., 2020. "Bayesian inference for Common cause failure rate based on causal inference with missing data," Reliability Engineering and System Safety, Elsevier, vol. 197(C).

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