sadists (version 0.1.0)

lambdap: The lambda prime distribution.

Description

Density, distribution function, quantile function and random generation for the lambda prime distribution.

Usage

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)

Arguments

x,q

vector of quantiles.

df

the degrees of freedom in the chi square. This is not recycled against the x,q,p,n.

t

the scaling parameter on the chi. This is not recycled against the x,q,p,n.

log

logical; if TRUE, densities $f$ are given as $\mbox{log}(f)$.

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 $\mbox{log}(p)$.

lower.tail

logical; if TRUE (default), probabilities are $P[X \le x]$, otherwise, $P[X > x]$.

Value

• 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.

Details

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 non-central t because $$t = \frac{Z' + T}{\sqrt{y/\nu}}$$

References

Lecoutre, Bruno. "Another look at confidence intervals for the noncentral t distribution." Journal of Modern Applied Statistical Methods 6, no. 1 (2007): 107--116. http://www.univ-rouen.fr/LMRS/Persopage/Lecoutre/telechargements/Lecoutre_Another_look-JMSAM2007_6(1).pdf

Lecoutre, Bruno. "Two useful distributions for Bayesian predictive procedures under normal models." Journal of Statistical Planning and Inference 79 (1999): 93--105.

See Also

t distribution functions, dt, pt, qt, rt, K prime distribution functions, dkprime, pkprime, qkprime, rkprime, upsilon distribution functions, dupsilon, pupsilon, qupsilon, rupsilon,

Examples

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)