Parameter estimation for generalized Dirichlet distributions from the sample estimates of the first and the second moments of random variables

Authors:
Tzu-Tsung Wong
Affiliations:
Institute of Information Management, National Cheng Kung University, 1, Ta-Sheuh Road, Tainan City 701, Taiwan, ROC
Venue:
Computational Statistics & Data Analysis
Year:
2010

Citing 5
Cited 2

Generalized Dirichlet distribution in Bayesian analysis

Applied Mathematics and Computation
High-Dimensional Unsupervised Selection and Estimation of a Finite Generalized Dirichlet Mixture Model Based on Minimum Message Length

IEEE Transactions on Pattern Analysis and Machine Intelligence
Discrete data clustering using finite mixture models

Pattern Recognition
Alternative prior assumptions for improving the performance of naïve Bayesian classifiers

Data Mining and Knowledge Discovery
A hybrid SEM algorithm for high-dimensional unsupervised learning using a finite generalized Dirichlet mixture

IEEE Transactions on Image Processing

The generalized dirichlet distribution in enhanced topic detection

Proceedings of the 21st ACM international conference on Information and knowledge management
Generalized Dirichlet priors for Naïve Bayesian classifiers with multinomial models in document classification

Data Mining and Knowledge Discovery

Quantified Score

Hi-index	0.03

Visualization

Abstract

Generalized Dirichlet distributions have a more flexible covariance structure than Dirichlet distributions, and the computation for the moments of a generalized Dirichlet distribution is still tractable. For situations under which Dirichlet distributions are inappropriate for data analysis, generalized Dirichlet distributions will generally be an applicable alternative. When the expected values and the covariance matrix of random variables can be estimated from available data, this study introduces ways to estimate the parameters of a generalized Dirichlet distribution for analyzing compositional data. Under the assumption that the sample mean of every variable must be considered for parameter estimation, we present methods for choosing the statistics from a sample covariance matrix to construct a generalized Dirichlet distribution. Some rules for removing inappropriate statistics from a sample covariance matrix to speed up the estimation process are also established. An example for Taiwan's car market is introduced to demonstrate the applicability of the parameter estimation methods.