Description Usage Arguments Details Value Note Author(s) See Also Examples
Density, distribution function, quantile function and random generation for the doubly non-central Eta distribution.
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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 non-centrality parameters for the numerator and denominator.
We do not recycle these versus 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 Gram-Charlier, Edeworth, or Cornish-Fisher 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]. |
Suppose Z is a normal with mean delta_1, and standard deviation 1, independent of X ~ X^2(delta_2,v_2), a non-central chi-square with v_2 degrees of freedom and non-centrality parameter delta_2. Then
Y = Z/sqrt(Z^2 + X)
takes a doubly non-central Eta distribution with v_2 degrees of freedom and non-centrality parameters delta_1,delta_2. The square of a doubly non-central Eta is a doubly non-central 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 non-central) t distribution functions,
ddnt, pdnt, qdnt, rdnt
.
(doubly non-central) Beta distribution functions,
ddnbeta, pdnbeta, qdnbeta, rdnbeta
.
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