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)
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.
vector of quantiles.
the degrees of freedom in the chi square.
This is not recycled against the x,q,p,n.
the scaling parameter on the chi.
This is not recycled against the x,q,p,n.
logical; if TRUE, densities \(f\) are given as \(\mbox{log}(f)\).
the order to use in the approximate density, distribution, and quantile computations, via the Gram-Charlier, Edeworth, or Cornish-Fisher expansion.
vector of probabilities.
number of observations.
logical; if TRUE, probabilities p are given as \(\mbox{log}(p)\).
logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).
Steven E. Pav shabbychef@gmail.com
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 $$t = \frac{Z' + T}{\sqrt{y/\nu}}$$
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.
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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