A Generalization of the Dirichlet Distribution
نویسنده
چکیده
This vignette is based on Hankin (2010). It discusses a generalization of the Dirichlet distribution, the ‘hyperdirichlet’, in which various types of incomplete observations may be incorporated. It is conjugate to the multinomial distribution when some observations are censored or grouped. The hyperdirichlet R package is introduced and examples given. A number of statistical tests are performed on the example datasets, which are drawn from diverse disciplines including sports statistics, the sociology of climate change, and psephology. This vignette is based on a manuscript currently under review at the Journal of Statistical Software. For reasons of performance, some of the more computationally expensive results are pre-loaded. To calculate them from scratch, change “calc_from_scratch <TRUE” to “calc_from_scratch <FALSE” in chunk time_saver.
منابع مشابه
The Dirichlet Process Mixture (DPM) Model
The Dirichlet distribution forms our first step toward understanding the DPM model. The Dirichlet distribution is a multi-parameter generalization of the Beta distribution and defines a distribution over distributions, i.e. the result of sampling a Dirichlet is a distribution on some discrete probability space. Let Θ = {θ1,θ2, . . . ,θn} be a probability distribution on the discrete space = { 1...
متن کاملSome Diffusion Processes Associated With Two Parameter Poisson-Dirichlet Distribution and Dirichlet Process
The two parameter Poisson-Dirichlet distribution PD(α, θ) is the distribution of an infinite dimensional random discrete probability. It is a generalization of Kingman’s Poisson-Dirichlet distribution. The two parameter Dirichlet process Πα,θ,ν0 is the law of a pure atomic random measure with masses following the two parameter Poisson-Dirichlet distribution. In this article we focus on the cons...
متن کاملIntroducing of Dirichlet process prior in the Nonparametric Bayesian models frame work
Statistical models are utilized to learn about the mechanism that the data are generating from it. Often it is assumed that the random variables y_i,i=1,…,n ,are samples from the probability distribution F which is belong to a parametric distributions class. However, in practice, a parametric model may be inappropriate to describe the data. In this settings, the parametric assumption could be r...
متن کاملOn The Dirichlet Distribution
The Dirichlet distribution is a multivariate generalization of the Beta distribution. It is an important multivariate continuous distribution in probability and statistics. In this report, we review the Dirichlet distribution and study its properties, including statistical and information-theoretic quantities involving this distribution. Also, relationships between the Dirichlet distribution an...
متن کاملA New Generalization of the Gompertz distribution
In this paper, a new distribution of the three-parameter lifetime model called the Marshall-Olkin Gompertz is proposed on the basis of the Gompertz distribution. It is a generalization of the Gompertz distribution having decreasing failure rate and can also be increasing and bathtub-shaped depending on its parameters. The probability density function, cumulative distribution function,...
متن کاملThe Dirichlet-Multinomial and Dirichlet-Categorical models for Bayesian inference
There are some pedagogical concerns to be noted. First, the pdf f(x) is technically defined only in (K−1)-dimensional space and not K; this is because SK has zero measure in K dimensions. Second, the support is actually the open simplex, meaning all xi > 0 (which implies no xi = 1). The Dirichlet distribution is a generalization of the Beta distribution, which is the conjugate prior for coin fl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010