dnt {sadists} | R Documentation |
The doubly non-central t distribution.
Description
Density, distribution function, quantile function and random generation for the doubly non-central t distribution.
Usage
ddnt(x, df, ncp1, ncp2, log = FALSE, order.max=6)
pdnt(q, df, ncp1, ncp2, lower.tail = TRUE, log.p = FALSE, order.max=6)
qdnt(p, df, ncp1, ncp2, lower.tail = TRUE, log.p = FALSE, order.max=6)
rdnt(n, df, ncp1, ncp2)
Arguments
x , q |
vector of quantiles. |
df |
the degrees of freedom for the denominator, |
ncp1 , ncp2 |
the non-centrality parameters for the numerator and denominator,
respectively, |
log |
logical; if TRUE, densities |
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 |
lower.tail |
logical; if TRUE (default), probabilities are
|
Details
Let Z \sim \mathcal{N}\left(\mu,1\right)
independently
of X \sim \chi^2\left(\theta,\nu\right)
. The
random variable
T = \frac{Z}{\sqrt{X/\nu}}
takes a doubly non-central t distribution with parameters
\nu, \mu, \theta
.
Value
ddnt
gives the density, pdnt
gives the
distribution function, qdnt
gives the quantile function,
and rdnt
generates random deviates.
Invalid arguments will result in return value NaN
with a warning.
Note
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.
Author(s)
Steven E. Pav shabbychef@gmail.com
References
Krishnan, Marakatha. "Series Representations of the Doubly Noncentral t-Distribution." Journal of the American Statistical Association 63, no. 323 (1968): 1004-1012.
See Also
t distribution functions, dt, pt, qt, rt
Examples
rvs <- rdnt(128, 20, 1, 1)
dvs <- ddnt(rvs, 20, 1, 1)
pvs.H0 <- pdnt(rvs, 20, 0, 1)
pvs.HA <- pdnt(rvs, 20, 1, 1)
plot(ecdf(pvs.H0))
plot(ecdf(pvs.HA))
# compare to singly non-central
dv1 <- ddnt(1, df=10, ncp1=5, ncp2=0, log=FALSE)
dv2 <- dt(1, df=10, ncp=5, log=FALSE)
pv1 <- pdnt(1, df=10, ncp1=5, ncp2=0, log.p=FALSE)
pv11 <- pdnt(1, df=10, ncp1=5, ncp2=0.001, log.p=FALSE)
v2 <- pt(1, df=10, ncp=5, log.p=FALSE)
q1 <- qdnt(pv1, df=10, ncp1=5, ncp2=0, log.p=FALSE)