dneta  R Documentation 
Density, distribution function, quantile function and random generation for the doubly noncentral Eta distribution.
ddneta(x, df, ncp1, ncp2, log = FALSE, order.max=6)
pdneta(q, df, ncp1, ncp2, lower.tail = TRUE, log.p = FALSE, order.max=6)
qdneta(p, df, ncp1, ncp2, lower.tail = TRUE, log.p = FALSE, order.max=6)
rdneta(n, df, ncp1, ncp2)
x, q 
vector of quantiles. 
df 
the degrees of freedom for the denominator chi square.
We do not recycle this versus the 
ncp1, ncp2 
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

Suppose Z
is a normal with mean \delta_1
,
and standard deviation 1, independent of
X \sim \chi^2\left(\delta_2,\nu_2\right)
,
a noncentral chisquare with \nu_2
degrees of freedom
and noncentrality parameter \delta_2
. Then
Y = \frac{Z}{\sqrt{Z^2 + X}}
takes a doubly noncentral Eta distribution with
\nu_2
degrees of freedom and noncentrality parameters
\delta_1,\delta_2
. The square of
a doubly noncentral Eta is a doubly noncentral Beta variate.
ddneta
gives the density, pdneta
gives the
distribution function, qdneta
gives the quantile function,
and rdneta
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
(doubly noncentral) t distribution functions,
ddnt, pdnt, qdnt, rdnt
.
(doubly noncentral) Beta distribution functions,
ddnbeta, pdnbeta, qdnbeta, rdnbeta
.
rv < rdneta(500, df=100,ncp1=1.5,ncp2=12)
d1 < ddneta(rv, df=100,ncp1=1.5,ncp2=12)
plot(rv,d1)
p1 < ddneta(rv, df=100,ncp1=1.5,ncp2=12)
# should be nearly uniform:
plot(ecdf(p1))
q1 < qdneta(ppoints(length(rv)), df=100,ncp1=1.5,ncp2=12)
qqplot(x=rv,y=q1)
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