prodnormal  R Documentation 
Density, distribution function, quantile function and random generation for the distribution of the product of indepdendent normal random variables.
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)
x, q 
vector of quantiles. 
mu 
the vector of means.
This is recycled against the 
sigma 
the vector of standard deviations.
This is recycled against the 
log 
logical; if TRUE, densities 
order.max 
the order to use in the approximate density, distribution, and quantile computations, via the GramCharlier, Edeworth, or CornishFisher expansion. 
p 
vector of probabilities. 
n 
number of observations. 
log.p 
logical; if TRUE, probabilities p are given
as 
lower.tail 
logical; if TRUE (default), probabilities are

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.
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.
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.
Steven E. Pav shabbychef@gmail.com
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)
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