prodnormal {sadists}

The product of normal random variates.

Description

Density, distribution function, quantile function and random generation for the distribution of the product of indepdendent normal random variables.

Usage

dprodnormal(x, mu, sigma, log = FALSE, order.max=5)

pprodnormal(q, mu, sigma, lower.tail = TRUE, log.p = FALSE, order.max=5)

qprodnormal(p, mu, sigma, lower.tail = TRUE, log.p = FALSE, order.max=5)

rprodnormal(n, mu, sigma)

Arguments

x, q

vector of quantiles.

mu

the vector of means. This is recycled against the sigma, but not against the x,q,p,n.

sigma

the vector of standard deviations. This is recycled against the mu, but not against the x,q,p,n.

log

logical; if TRUE, densities f are given as \mbox{log}(f).

order.max

the order to use in the approximate density, distribution, and quantile computations, via the Gram-Charlier, Edeworth, or Cornish-Fisher expansion.

p

vector of probabilities.

n

number of observations.

log.p

logical; if TRUE, probabilities p are given as \mbox{log}(p).

lower.tail

logical; if TRUE (default), probabilities are P[X \le x], otherwise, P[X > x].

Details

Let Z_i \sim \mathcal{N}\left(\mu_i, \sigma_i^2\right) be independently distributed normal variates, with means \mu_i and variances \sigma_i^2. Suppose

Y = \prod_i Z_i.

Then Y follows a product of normals distribution.

Value

dprodnormal gives the density, pprodnormal gives the distribution function, qprodnormal gives the quantile function, and rprodnormal generates random deviates.

Invalid arguments will result in return value NaN with a warning.

Note

The PDF, CDF, and quantile function are approximated, via the Edgeworth or Cornish Fisher approximations, which may not be terribly accurate in the tails of the distribution. You are warned.

The distribution parameters are not recycled with respect to the x, p, q or n parameters, for, respectively, the density, distribution, quantile and generation functions. This is for simplicity of implementation and performance. It is, however, in contrast to the usual R idiom for dpqr functions.

Author(s)

Steven E. Pav [e-mail]

Examples

mu <- c(100,20,10)
sigma <- c(10,50,10)
rvs <- rprodnormal(128, mu, sigma)
dvs <- dprodnormal(rvs, mu, sigma)
qvs <- pprodnormal(rvs, mu, sigma)
pvs <- qprodnormal(ppoints(length(rvs)), mu, sigma)