dnt: Non-central t-Distribution Density

Description

dntJKBm is a fully Rmpfr-ified vectorized version of dntJKBf() from DPQ; see there.

dtWVm(x, df, ncp) computes the density function $f (x)$ of the t distribution with df degrees of freedom and non-centrality parameter ncp, according to Wolfgang Viechtbauer's proposal in 2002, using an asymptotic formula for “large” df $= ν$ .

Usage

dntJKBm(x, df, ncp, log = FALSE, M = 1000) # __ Deprecated __ use DPQ :: dntJKBf
dtWVm  (x, df, ncp, log = FALSE)

Value

an mpfr vector of the same length as the maximum of the lengths of x, df, ncp.

Arguments

x: numeric or "mpfr" vector.
df: degrees of freedom ( $> 0$ , maybe non-integer). df = Inf is allowed.
ncp: non-centrality parameter $δ$ ; If omitted, use the central t distribution.
log: as in dt(), a logical indicating if $\log (f (x, *))$ should be returned instead of $f (x, *)$ .
M: the number of terms to be used, a positive integer.

Author

Martin Maechler

Details

See dtWV's details (package DPQ).

As DPQ's dntJKBf() is already fully mpfr-ized, dntJKBm() is deprecated.

Examples

Run this code

tt <- seq(0, 10, len = 21)
ncp <- seq(0, 6, len = 31)
dt3R  <- outer(tt, ncp, dt  , df = 3)
dt3WV <- outer(tt, ncp, dtWVm, df = 3)
all.equal(dt3R, dt3WV) # rel.err 0.00063
dt25R  <- outer(tt, ncp, dt  , df = 25)
dt25WV <- outer(tt, ncp, dtWVm, df = 25)
all.equal(dt25R, dt25WV) # rel.err 1.1e-5

x <- -10:700
fx  <- dt  (x, df = 22, ncp =100)
lfx <- dt  (x, df = 22, ncp =100, log=TRUE)
lfV <- dtWVm(x, df = 22, ncp =100, log=TRUE)

head(lfx, 15) # shows that R's dt(*, log=TRUE) implementation is "quite suboptimal"

## graphics
opa <- par(no.readonly=TRUE)
par(mar=.1+c(5,4,4,3), mgp = c(2, .8,0))
plot(fx ~ x, type="l")
par(new=TRUE) ; cc <- c("red", adjustcolor("orange", 0.4))
plot(lfx ~ x, type = "o", pch=".", col=cc[1], cex=2, ann=FALSE, yaxt="n")
sfsmisc::eaxis(4, col=cc[1], col.axis=cc[1], small.args = list(col=cc[1]))
lines(x, lfV, col=cc[2], lwd=3)
dtt1 <- "      dt"; dtt2 <- "(x, df=22, ncp=100"; dttL <- paste0(dtt2,", log=TRUE)")
legend("right", c(paste0(dtt1,dtt2,")"), paste0(c(dtt1,"dtWVm"), dttL)),
       lty=1, lwd=c(1,1,3), col=c("black", cc), bty = "n")
par(opa) # reset


## For dntJKBm(), see  example(dntJKBf, package="DPQ")

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