Categorical Distribution
This is the density and random deviates function for the categorical distribution with probabilities parameter p.
dcat(x, p, log=FALSE) qcat(pr, p, lower.tail=TRUE, log.pr=FALSE) rcat(n, p)
x |
This is a vector of discrete data with k discrete
categories, and is of length n. This function also accepts
x after it has been converted to an n x k
indicator matrix, such as with the |
n |
This is the number of observations, which must be a positive
integer that has length 1. When |
p |
This is a vector of length k or n x k
matrix of probabilities. The |
pr |
This is a vector of probabilities, or log-probabilities. |
log |
Logical. If |
log.pr |
Logical. if |
lower.tail |
Logical. if |
Application: Discrete Univariate
Density: p(theta) = Sum (theta * p)
Inventor: Unknown (to me, anyway)
Notation 1: theta ~ CAT(p)
Notation 2: p(theta) = CAT(theta | p)
Parameter 1: probabilities p
Mean: E(theta) = Unknown
Variance: var(theta) = Unknown
Mode: mode(theta) = Unknown
Also called the discrete distribution, the categorical distribution describes the result of a random event that can take on one of k possible outcomes, with the probability p of each outcome separately specified. The vector p of probabilities for each event must sum to 1. The categorical distribution is often used, for example, in the multinomial logit model. The conjugate prior is the Dirichlet distribution.
dcat gives the density and
rcat generates random deviates.
Statisticat, LLC. software@bayesian-inference.com
library(LaplacesDemon) dcat(x=1, p=c(0.3,0.3,0.4)) rcat(n=10, p=c(0.1,0.3,0.6))
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