qtR {DPQ}

Pure R Implementation of R's C-level t-Distribution Quantiles qt()

Description

A pure R implementation of R's Mathlib own C-level qt() function.
qtR() is simply defined as

qtR <- Vectorize(qtR1, c("p","df"))

where in qtR1(p, df, *) both p and df must be of length one.

Usage

qtR1(p, df, lower.tail = TRUE, log.p = FALSE,
     eps = 1e-12, d1_accu = 1e-13, d1_eps = 1e-11,
     itNewt = 10L, epsNewt = 1e-14, logNewton = log.p,
     verbose = FALSE)
qtR (p, df, lower.tail = TRUE, log.p = FALSE,
     eps = 1e-12, d1_accu = 1e-13, d1_eps = 1e-11,
     itNewt = 10L, epsNewt = 1e-14, logNewton = log.p,
     verbose = FALSE)

Arguments

p, df

vectors of probabilities and degrees of freedom, see qt.

lower.tail, log.p

logical; see qt.

eps

non-negative tolerance for checking if df is “very close” to 1 or 2, respectively (when a special branch will be chosen).

d1_accu, d1_eps

non-negative tolerances only for the df < 1 cases.

itNewt

integer, the maximal number of final Newton(-Raphson) steps.

epsNewt

non-negative convergence tolerance for the final Newton steps.

logNewton

logical, in case of log.p=TRUE indicating if final Newton steps should happen in log-scale.

verbose

logical indicating if diagnostic console output should be produced.

Value

numeric vector of t quantiles, properly recycled in (p, df).

Author(s)

Martin Maechler

See Also

qtU and R's qt.

Examples

## Inspired from Bugzilla PR#16380
pxy <- curve(pt(-x, df = 1.09, log.p = TRUE), 4e152, 1e156, log="x", n=501)
qxy <- curve(-qt(x, df = 1.09, log.p = TRUE), -392, -385, n=501, log="y", col=4, lwd=2)
lines(x ~ y, data=pxy, col = adjustcolor(2, 1/2), lwd=5, lty=3)
## now our "pure R" version:

qRy <- -qtR(qxy$x, df = 1.09, log.p = TRUE)
all.equal(qRy, qxy$y) # "'is.NA' value mismatch: 14 in current 0 in target" for R <= 4.2.1
cbind(as.data.frame(qxy), qRy, D = qxy$y - qRy)
plot((y - qRy) ~ x, data = qxy, type="o", cex=1/4)

qtR1(.1, .1, verbose=TRUE)
pt(qtR(-390.5, df=1.10, log.p=TRUE, verbose=TRUE, itNewt = 100), df=1.10, log.p=TRUE)/-390.5 - 1
## qt(p=     -390.5, df=        1.1, *) -- general case
##  -> P=2.55861e-170, neg=TRUE, is_neg_lower=TRUE; -> final P=5.11723e-170
## usual 'df' case:  P_ok:= P_ok1 = TRUE, y=3.19063e-308, P..., !P_ok: log.p2=-390.5, y=3.19063e-308
## !P_ok && x < -36.04: q=5.87162e+153
## P_ok1: log-scale Taylor (iterated):
## it= 1, .. d{q}1=exp(lF - dt(q,df,log=T))*(lF - log(P/2)) = -5.03644e+152; n.q=5.36798e+153
## it= 2, .. d{q}1=exp(lF - dt(q,df,log=T))*(lF - log(P/2)) =  2.09548e+151; n.q=5.38893e+153
## it= 3, .. d{q}1=exp(lF - dt(q,df,log=T))*(lF - log(P/2)) =  4.09533e+148; n.q=5.38897e+153
## it= 4, .. d{q}1=exp(lF - dt(q,df,log=T))*(lF - log(P/2)) =   1.5567e+143; n.q=5.38897e+153
## [1] 0
##    === perfect!
pt(qtR(-391, df=1.10, log.p=TRUE, verbose=TRUE),
   df=1.10, log.p=TRUE)/-391 - 1 # now perfect