rmixture: Simulation from Discrete Mixtures

Description

Generate random variates from a discrete mixture of distributions.

Usage

rmixture(n, probs, models, shuffle = TRUE)

Value

A vector of random variates from the mixture with density $f (x)$ .

Arguments

n: number of random variates to generate. If length(n) > 1, the length is taken to be the number required.
probs: numeric non-negative vector specifying the probability for each model; is internally normalized to sum 1. Infinite and missing values are not allowed. Values are recycled as necessary to match the length of models.
models: vector of expressions specifying the simulation models with the number of variates omitted; see Details. Models are recycled as necessary to match the length of probs.
shuffle: logical; should the random variates from the distributions be shuffled?

Author

Vincent Goulet vincent.goulet@act.ulaval.ca

Details

rmixture generates variates from a discrete mixture, that is the random variable with a probability density function of the form $f (x) = p_{1} f_{1} (x) + . . . + p_{n} f_{n} (x),$ where $f_{1}, \dots, f_{n}$ are densities and $\sum_{i = 1}^{n} p_{i} = 1$ .

The values in probs will be internally normalized to be used as probabilities $p_{1} + \dots + p_{n}$ .

The specification of simulation models uses the syntax of rcomphierarc. Models $f_{1}, \dots, f_{n}$ are expressed in a semi-symbolic fashion using an object of mode expression where each element is a complete call to a random number generation function, with the number of variates omitted.

The argument of the random number generation functions for the number of variates to simulate must be named n.

If shuffle is FALSE, the output vector contains all the random variates from the first model, then all the random variates from the second model, and so on. If the order of the variates is irrelevant, this cuts the time to generate the variates roughly in half.

Examples

Run this code

## Mixture of two exponentials (with means 1/3 and 1/7) with equal
## probabilities.
rmixture(10, 0.5, expression(rexp(3), rexp(7)))
rmixture(10, 42, expression(rexp(3), rexp(7))) # same

## Mixture of two lognormals with different probabilities.
rmixture(10, probs = c(0.55, 0.45),
         models = expression(rlnorm(3.6, 0.6),
                             rlnorm(4.6, 0.3)))

## Building the model expressions in the following example
## works as 'rate' is defined in the parent frame of
## 'rmixture'.
probs <- c(2, 5)
g <- function(n, p, rate)
    rmixture(n, p, expression(rexp(rate[1]), rexp(rate[2])))
g(10, probs, c(3, 7))

## The following example does not work: 'rate' does not exist
## in the evaluation frame of 'rmixture'.
f <- function(n, p, model) rmixture(n, p, model)
h <- function(n, p, rate)
    f(n, p, expression(rexp(rate[1]), rexp(rate[2])))
if (FALSE) h(10, probs, c(3, 7))

## Fix: substitute the values in the model expressions.
h <- function(n, p, rate)
{
    models <- eval(substitute(expression(rexp(a[1]), rexp(a[2])),
                              list(a = rate)))
    f(n, p, models)
}
h(10, probs, c(3, 7))

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