proddnf  R Documentation 
Density, distribution function, quantile function and random generation for the product of multiple independent doubly noncentral F variates.
dproddnf(x, df1, df2, ncp1, ncp2, log = FALSE, order.max=4)
pproddnf(q, df1, df2, ncp1, ncp2, lower.tail = TRUE, log.p = FALSE, order.max=4)
qproddnf(p, df1, df2, ncp1, ncp2, lower.tail = TRUE, log.p = FALSE, order.max=4)
rproddnf(n, df1, df2, ncp1, ncp2)
x, q 
vector of quantiles. 
df1, df2 
the vectors of the degrees of freedom for the numerator and denominator.
We do not recycle these versus the 
ncp1, ncp2 
the vectors of the noncentrality parameters for the numerator and denominator.
We do not recycle these versus 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_j \sim F\left(\delta_{1,j},\delta_{2,j},\nu_{1,j},\nu_{2,j}\right)
be independent doubly noncentral F variates with noncentrality parameters
\delta_{i,j}
and degrees of freedom
\nu_{i,j}
for i=1,2,\ldots,I
and
j=1,2
.
Then
Y = \prod_j x_j
takes a product of doubly noncentral F's distribution. We take the
parameters of this distribution as the four I
length vectors
of the two degrees of freedom and the two noncentrality parameters.
dproddnf
gives the density, pproddnf
gives the
distribution function, qproddnf
gives the quantile function,
and rproddnf
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 shabbychef@gmail.com
Pav, Steven. Moments of the log noncentral chisquare distribution. https://arxiv.org/abs/1503.06266
The sum of log of chisquares distribution,
dsumlogchisq
,
psumlogchisq
,
qsumlogchisq
,
rsumlogchisq
.
(doubly noncentral) F distribution functions,
ddnf
,
pdnf
,
qdnf
,
rdnf
.
df1 < c(10,20,5)
df2 < c(1000,500,150)
ncp1 < c(1,0,2.5)
ncp2 < c(0,1.5,5)
rv < rproddnf(500, df1=df1,df2=df2,ncp1=ncp1,ncp2=ncp2)
d1 < dproddnf(rv, df1=df1,df2=df2,ncp1=ncp1,ncp2=ncp2)
plot(rv,d1)
p1 < pproddnf(rv, df1=df1,df2=df2,ncp1=ncp1,ncp2=ncp2)
# should be nearly uniform:
plot(ecdf(p1))
q1 < qproddnf(ppoints(length(rv)), df1=df1,df2=df2,ncp1=ncp1,ncp2=ncp2)
qqplot(x=rv,y=q1)
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