dnt  R Documentation 
Density, distribution function, quantile function and random generation for the doubly noncentral t distribution.
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)
x, q 
vector of quantiles. 
df 
the degrees of freedom for the denominator, 
ncp1, ncp2 
the noncentrality 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 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 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 noncentral t distribution with parameters
\nu, \mu, \theta
.
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.
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
Krishnan, Marakatha. "Series Representations of the Doubly Noncentral tDistribution." Journal of the American Statistical Association 63, no. 323 (1968): 10041012.
t distribution functions, dt, pt, qt, rt
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 noncentral
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)
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