sumchisqpow  R Documentation 
Density, distribution function, quantile function and random generation for the distribution of the weighted sum of noncentral chisquares taken to powers.
dsumchisqpow(x, wts, df, ncp=0, pow=1, log = FALSE, order.max=6)
psumchisqpow(q, wts, df, ncp=0, pow=1, lower.tail = TRUE, log.p = FALSE, order.max=6)
qsumchisqpow(p, wts, df, ncp=0, pow=1, lower.tail = TRUE, log.p = FALSE, order.max=6)
rsumchisqpow(n, wts, df, ncp=0, pow=1)
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 
pow 
the vector of the power 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
and p_i
be given constants. Suppose
Y = \sum_i w_i X_i^{p_i}.
Then Y
follows a weighted sum of chisquares to power distribution.
dsumchisqpow
gives the density, psumchisqpow
gives the
distribution function, qsumchisqpow
gives the quantile function,
and rsumchisqpow
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 'sum of chisquare power' distribution does not generalize the 'chibarsquare' distribution, whose density is the sum of chisquare densities.
Steven E. Pav shabbychef@gmail.com
The upsilon distribution,
dupsilon,pupsilon,qupsilon,rupsilon
.
wts < c(1,3,4)
df < c(100,20,10)
ncp < c(5,3,1)
pow < c(1,0.5,1)
rvs < rsumchisqpow(128, wts, df, ncp, pow)
dvs < dsumchisqpow(rvs, wts, df, ncp, pow)
qvs < psumchisqpow(rvs, wts, df, ncp, pow)
pvs < qsumchisqpow(ppoints(length(rvs)), wts, df, ncp, pow)
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