sadists (version 0.2.0)

dnbeta: The doubly non-central Beta distribution.

Description

Density, distribution function, quantile function and random generation for the doubly non-central Beta distribution.

Usage

ddnbeta(x, df1, df2, ncp1, ncp2, log = FALSE, order.max=6)
pdnbeta(q, df1, df2, ncp1, ncp2, lower.tail = TRUE, log.p = FALSE, order.max=6)
qdnbeta(p, df1, df2, ncp1, ncp2, lower.tail = TRUE, log.p = FALSE, order.max=6)
rdnbeta(n, df1, df2, ncp1, ncp2)

Arguments

x,q

vector of quantiles.

df1,df2

the degrees of freedom for the numerator and denominator. We do not recycle these versus the x,q,p,n.

ncp1,ncp2

the non-centrality parameters for the numerator and denominator. We do not recycle these versus 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

• ddnbeta gives the density, pdnbeta gives the distribution function, qdnbeta gives the quantile function, and rdnbeta generates random deviates.

  Invalid arguments will result in return value NaN with a warning.

Details

Suppose $x_i \sim \chi^2\left(\delta_i,\nu_i\right)$ be independent non-central chi-squares for $i=1,2$. Then $$Y = \frac{x_1}{x_1 + x_2}$$ takes a doubly non-central Beta distribution with degrees of freedom $\nu_1, \nu_2$ and non-centrality parameters $\delta_1,\delta_2$.

See Also

(doubly non-central) F distribution functions, ddnf, pdnf, qdnf, rdnf.

Examples

rv <- rdnbeta(500, df1=100,df2=500,ncp1=1.5,ncp2=12)
d1 <- ddnbeta(rv, df1=100,df2=500,ncp1=1.5,ncp2=12)
plot(rv,d1)
p1 <- ddnbeta(rv, df1=100,df2=500,ncp1=1.5,ncp2=12)
# should be nearly uniform:
plot(ecdf(p1))
q1 <- qdnbeta(ppoints(length(rv)), df1=100,df2=500,ncp1=1.5,ncp2=12)
qqplot(x=rv,y=q1)