Description Usage Arguments Details Value Note Author(s) References See Also Examples
Density, distribution function, quantile function and random generation for the distribution of the product of noncentral chisquares taken to powers.
1 2 3 4 5 6 7  dprodchisqpow(x, df, ncp=0, pow=1, log = FALSE, order.max=5)
pprodchisqpow(q, df, ncp=0, pow=1, lower.tail = TRUE, log.p = FALSE, order.max=5)
qprodchisqpow(p, df, ncp=0, pow=1, lower.tail = TRUE, log.p = FALSE, order.max=5)
rprodchisqpow(n, df, ncp=0, pow=1)

x, q 
vector of quantiles. 
df 
the vector of degrees of freedom.
This is recycled against the 
ncp 
the vector of noncentrality parameters.
This is recycled against the 
pow 
the vector of the power parameters.
This is recycled against the 
log 
logical; if TRUE, densities f are given as log(f). 
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 log(p). 
lower.tail 
logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]. 
Let X_i ~ chi^2(delta_i, v_i) be independently distributed noncentral chisquares, where v_i are the degrees of freedom, and delta_i are the noncentrality parameters. Let p_i be given constants. Suppose
Y = prod w_i (X_i)^(p_i).
Then Y follows a product of chisquares to power distribution.
dprodchisqpow
gives the density, pprodchisqpow
gives the
distribution function, qprodchisqpow
gives the quantile function,
and rprodchisqpow
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.
The PDQ functions are computed by translation of the sum of log chisquares distribution functions.
Steven E. Pav [email protected]
Pav, Steven. Moments of the log noncentral chisquare distribution. http://arxiv.org/abs/1503.06266
The sum of log of chisquares distribution,
dsumlogchisq
,
psumlogchisq
,
qsumlogchisq
,
rsumlogchisq
,
The upsilon distribution,
dupsilon
,
pupsilon
,
qupsilon
,
rupsilon
.
The sum of chisquare powers distribution,
dsumchisqpow
,
psumchisqpow
,
qsumchisqpow
,
rsumchisqpow
.
1 2 3 4 5 6 7  df < c(100,20,10)
ncp < c(5,3,1)
pow < c(1,0.5,1)
rvs < rprodchisqpow(128, df, ncp, pow)
dvs < dprodchisqpow(rvs, df, ncp, pow)
qvs < pprodchisqpow(rvs, df, ncp, pow)
pvs < qprodchisqpow(ppoints(length(rvs)), df, ncp, pow)

Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.