| dist.Normal.Mixture {LaplacesDemon} | R Documentation |
These functions provide the density, cumulative, and random generation for the mixture of univariate normal distributions with probability p, mean mu and standard deviation sigma.
dnormm(x, p, mu, sigma, log=FALSE) pnormm(q, p, mu, sigma, lower.tail=TRUE, log.p=FALSE) rnormm(n, p, mu, sigma)
x,q |
This is vector of values at which the density will be evaluated. |
p |
This is a vector of length M of probabilities for M components. The sum of the vector must be one. |
n |
This is the number of observations, which must be a positive integer that has length 1. |
mu |
This is a vector of length M that is the mean parameter mu. |
sigma |
This is a vector of length M that is the standard deviation parameter sigma, which must be positive. |
lower.tail |
Logical. This defaults to |
log,log.p |
Logical. If |
Application: Continuous Univariate
Density: p(theta) = sum p[i] N(mu[i], sigma[i]^2)
Inventor: Unknown
Notation 1: theta ~ N(mu, sigma^2)
Notation 2: p(theta) = N(theta | mu, sigma^2)
Parameter 1: mean parameters mu
Parameter 2: standard deviation parameters sigma > 0
Mean: E(theta) = sum p[i] mu[i]
Variance: var(theta) = sum p[i] sigma[i]^(0.5)
Mode:
A mixture distribution is a probability distribution that is a combination of other probability distributions, and each distribution is called a mixture component, or component. A probability (or weight) exists for each component, and these probabilities sum to one. A mixture distribution (though not these functions here in particular) may contain mixture components in which each component is a different probability distribution. Mixture distributions are very flexible, and are often used to represent a complex distribution with an unknown form. When the number of mixture components is unknown, Bayesian inference is the only sensible approach to estimation.
A normal mixture, or Gaussian mixture, distribution is a combination of normal probability distributions.
dnormm gives the density,
pnormm returns the CDF, and
rnormm generates random deviates.
Statisticat, LLC. software@bayesian-inference.com
ddirichlet and
dnorm.
library(LaplacesDemon) p <- c(0.3,0.3,0.4) mu <- c(-5, 1, 5) sigma <- c(1,2,1) x <- seq(from=-10, to=10, by=0.1) plot(x, dnormm(x, p, mu, sigma, log=FALSE), type="l") #Density plot(x, pnormm(x, p, mu, sigma), type="l") #CDF plot(density(rnormm(10000, p, mu, sigma))) #Random Deviates