lambdap  R Documentation 
Density, distribution function, quantile function and random generation for the lambda prime distribution.
dlambdap(x, df, t, log = FALSE, order.max=6)
plambdap(q, df, t, lower.tail = TRUE, log.p = FALSE, order.max=6)
qlambdap(p, df, t, lower.tail = TRUE, log.p = FALSE, order.max=6)
rlambdap(n, df, t)
x, q 
vector of quantiles. 
df 
the degrees of freedom in the chi square.
This is not recycled against the 
t 
the scaling parameter on the chi.
This is not recycled against 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 y \sim \chi^2\left(\nu\right)
, and
Z
is a standard normal.
T = Z + t \sqrt{y/\nu}
takes a lambda prime distribution with parameters
\nu, t
.
A lambda prime random variable can be viewed as a confidence
level on a noncentral t because
t = \frac{Z' + T}{\sqrt{y/\nu}}
dlambdap
gives the density, plambdap
gives the
distribution function, qlambdap
gives the quantile function,
and rlambdap
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
Lecoutre, Bruno. "Another look at confidence intervals for the noncentral t distribution." Journal of Modern Applied Statistical Methods 6, no. 1 (2007): 107–116. https://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=1128&context=jmasm
Lecoutre, Bruno. "Two useful distributions for Bayesian predictive procedures under normal models." Journal of Statistical Planning and Inference 79 (1999): 93–105.
t distribution functions, dt, pt, qt, rt
,
K prime distribution functions, dkprime, pkprime, qkprime, rkprime
,
upsilon distribution functions, dupsilon, pupsilon, qupsilon, rupsilon
,
rv < rlambdap(100, 50, t=0.01)
d1 < dlambdap(1, 50, t=0.01)
pv < plambdap(rv, 50, t=0.01)
qv < qlambdap(ppoints(length(rv)), 50, t=1)
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