"This book provides a comprehensive review on the Dirichlet distribution including its basic properties, marginal and conditional distributions, cumulative distribution and survival functions. The authors provide insight into new materials such as survival function, characteristic functions for two uniform distributions over the hyper-plane and simplex distribution for linear function of Dirichlet components estimation via the expectation-maximization gradient algorithm and application. Two new families of distributions (GDD and NDD) are explored, with emphasis on applications in incomplete categorical data and survey data with non-response. Theoretical results on inverted Dirichlet distribution and its applications are featured along with new results that deal with truncated Dirichlet distribution, Dirichlet process and smoothed Dirichlet distribution. The final chapters look at results gathered for Dirichlet-multinomial distribution, Generalized Dirichlet distribution, Liouville distribution, generalized Liouville distribution and matrix-variate Dirichlet distribution"--