Description Usage Arguments Details Value Note Author(s) See Also Examples
Density, distribution function, quantile function and random generation for the doubly non-central Beta distribution.
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x, q |
vector of quantiles. |
df1, df2 |
the degrees of freedom for the numerator and denominator.
We do not recycle these 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 x_i ~ X^2(delta_i,v_i) be independent non-central chi-squares for i=1,2. Then
Y = x_1 / (x_1 + x_2)
takes a doubly non-central Beta distribution with degrees of freedom v_1, v_2 and non-centrality parameters delta_1,delta_2.
ddnbeta
gives the density, pdnbeta
gives the
distribution function, qdnbeta
gives the quantile function,
and rdnbeta
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) F distribution functions,
ddnf, pdnf, qdnf, rdnf
.
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