qbetaAppr {DPQ}

Compute (Approximate) Quantiles of the Beta Distribution

Description

Compute quantiles (inverse distribution values) of the beta distribution, using diverse approximations.

Usage

qbetaAppr.1(a, p, q, lower.tail=TRUE, log.p=FALSE,
            y = qnormUappr(a, lower.tail=lower.tail, log.p=log.p))

qbetaAppr.2(a, p, q, lower.tail=TRUE, log.p=FALSE, logbeta = lbeta(p,q))
qbetaAppr.3(a, p, q, lower.tail=TRUE, log.p=FALSE, logbeta = lbeta(p,q))
qbetaAppr.4(a, p, q, lower.tail=TRUE, log.p=FALSE,
            y = qnormUappr(a, lower.tail=lower.tail, log.p=log.p),
            verbose = getOption("verbose"))

qbetaAppr  (a, p, q, lower.tail=TRUE, log.p=FALSE,
            y = qnormUappr(a, lower.tail=lower.tail, log.p=log.p),
            logbeta = lbeta(p,q),
            verbose = getOption("verbose") && length(a) == 1)

qbeta.R    (alpha, p, q,
            lower.tail = TRUE, log.p = FALSE,
	    logbeta = lbeta(p,q),
	    low.bnd = 3e-308, up.bnd = 1-2.22e-16,
            method = c("AS109", "Newton-log"),
            tol.outer = 1e-15,
	    f.acu = function(a,p,q) max(1e-300, 10^(-13- 2.5/pp^2 - .5/a^2)),
	    fpu = .Machine$ double.xmin,
	    qnormU.fun = function(u, lu) qnormUappr(p=u, lp=lu)
          , R.pre.2014 = FALSE
	  , verbose = getOption("verbose")
          , non.finite.report = verbose
           )

Arguments

a, alpha

vector of probabilities (otherwise, e.g., in qbeta(), called p).

p, q

the two shape parameters of the beta distribution; otherwise, e.g., in qbeta(), called shape1 and shape2.

y

an approximation to \Phi^{-1}(1-\alpha) (aka z_{1-\alpha}) where \Phi(x) is the standard normal cumulative probability function and \Phi{-1}(x) its inverse, i.e., R's qnorm(x).

lower.tail, log.p

logical, see, e.g., qchisq(); must have length 1.

logbeta

must be lbeta(p,q); mainly an option to pass a value already computed.

verbose

logical or integer indicating if and how much “monitoring” information should be produced by the algorithm.

low.bnd, up.bnd

lower and upper bounds for ...TODO...

method

a string specifying the approximation method to be used.

tol.outer

the “outer loop” convergence tolerance; the default 1e-15 has been hardwired in R's qbeta().

f.acu

a function with arguments (a,p,q) ...TODO...

fpu

a very small positive number.

qnormU.fun

a function with arguments (u,lu) to compute “the same” as qnormUappr(), the upper standard normal quantile.

R.pre.2014

a logical ... TODO ...

non.finite.report

logical indicating if during the “outer loop” refining iterations, if y becomes non finite and the iterations have to stop, it should be reported (before the current best value is returned).

Value

...

Author(s)

The R Core Team for the C version of qbeta in R's sources; Martin Maechler for the R port, and the approximations.

See Also

qbeta.

Examples

 qbeta.R(0.6, 2, 3) # 0.4445
 qbeta.R(0.6, 2, 3) - qbeta(0.6, 2,3) # almost 0

 qbetaRV <- Vectorize(qbeta.R, "alpha") # now can use
 curve(qbetaRV(x, 1.5, 2.5))
 curve(qbeta  (x, 1.5, 2.5), add=TRUE, lwd = 3, col = adjustcolor("red", 1/2))

 ## an example of disagreement (and doubt, as borderline, close to underflow):
 qbeta.R(0.5078, .01, 5) # ->  2.77558e-15    # but
 qbeta  (0.5078, .01, 5) # now gives 4.651188e-31  -- correctly!
 qbeta  (0.5078, .01, 5, ncp=0)# ditto
 ## which is because qbeta() now works in log-x scale here:
 curve(pbeta(x, .01, 5), 1e-40, 1, n=10001, log="x", xaxt="n")
 sfsmisc::eaxis(1); abline(h=.5078, lty=3); abline(v=4.651188e-31,col=2)