dist.Laplace.Mixture {LaplacesDemon} | R Documentation |
Mixture of Laplace Distributions
Description
These functions provide the density, cumulative, and random generation
for the mixture of univariate Laplace distributions with probability
p
, location \mu
and scale \sigma
.
Usage
dlaplacem(x, p, location, scale, log=FALSE)
plaplacem(q, p, location, scale)
rlaplacem(n, p, location, scale)
Arguments
x , q |
This is vector of values at which the density will be evaluated. |
p |
This is a vector of length |
n |
This is the number of observations, which must be a positive integer that has length 1. |
location |
This is a vector of length |
scale |
This is a vector of length |
log |
Logical. If |
Details
Application: Continuous Univariate
Density:
p(\theta) = \sum p_i \mathcal{L}(\mu_i, \sigma_i)
Inventor: Unknown
Notation 1:
\theta \sim \mathcal{L}(\mu, \sigma)
Notation 2:
p(\theta) = \mathcal{L}(\theta | \mu, \sigma)
Parameter 1: location parameters
\mu
Parameter 2: scale parameters
\sigma > 0
Mean:
E(\theta) = \sum p_i \mu_i
Variance:
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 Laplace mixture distribution is a combination of Laplace probability distributions.
One of many applications of Laplace mixture distributions is the Laplace Mixture Model (LMM).
Value
dlaplacem
gives the density,
plaplacem
returns the CDF, and
rlaplacem
generates random deviates.
Author(s)
Statisticat, LLC. software@bayesian-inference.com
See Also
ddirichlet
and
dlaplace
.
Examples
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, dlaplacem(x, p, mu, sigma, log=FALSE), type="l") #Density
plot(x, plaplacem(x, p, mu, sigma), type="l") #CDF
plot(density(rlaplacem(10000, p, mu, sigma))) #Random Deviates