sumlogchisq  R Documentation 
Density, distribution function, quantile function and random generation for the distribution of the weighted sum of logs of noncentral chisquares.
dsumlogchisq(x, wts, df, ncp=0, log = FALSE, order.max=6)
psumlogchisq(q, wts, df, ncp=0, lower.tail = TRUE, log.p = FALSE, order.max=6)
qsumlogchisq(p, wts, df, ncp=0, lower.tail = TRUE, log.p = FALSE, order.max=6)
rsumlogchisq(n, wts, df, ncp=0)
x, q 
vector of quantiles. 
wts 
the vector of weights.
This is recycled against the 
df 
the vector of degrees of freedom.
This is recycled against the 
ncp 
the vector of noncentrality parameters.
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 X_i \sim \chi^2\left(\delta_i, \nu_i\right)
be independently distributed noncentral chisquares, where \nu_i
are the degrees of freedom, and \delta_i
are the
noncentrality parameters.
Let w_i
be given constants. Suppose
Y = \sum_i w_i \log X_i.
Then Y
follows a weighted sum of log of chisquares distribution.
dsumlogchisq
gives the density, psumlogchisq
gives the
distribution function, qsumlogchisq
gives the quantile function,
and rsumlogchisq
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
Pav, Steven. Moments of the log noncentral chisquare distribution. https://arxiv.org/abs/1503.06266
The product of chisquares to a power,
dprodchisqpow
,
pprodchisqpow
,
qprodchisqpow
,
rprodchisqpow
.
wts < c(1,3,4)
df < c(100,20,10)
ncp < c(5,3,1)
rvs < rsumlogchisq(128, wts, df, ncp)
dvs < dsumlogchisq(rvs, wts, df, ncp)
qvs < psumlogchisq(rvs, wts, df, ncp)
pvs < qsumlogchisq(ppoints(length(rvs)), wts, df, ncp)
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