TDist | R Documentation |
Density, distribution function, quantile function and random generation for the generalised t distribution with df degrees of freedom, using location and scale, or mean and sd. These are wrappers for stats::dt
, etc.
Note: In earlier versions of wiqid
the scale
argument to *t2
functions was incorrectly named sd
; they are not the same. These function now give a warning with the correct value of the sd
. New *t3
functions do use sd
which is only defined for df > 2
.
dt2(x, location, scale, df) pt2(x, location, scale, df, lower.tail=TRUE, log.p=FALSE) qt2(p, location, scale, df, lower.tail=TRUE, log.p=FALSE) rt2(n, location, scale, df) dt3(x, mean, sd, df) pt3(x, mean, sd, df, lower.tail=TRUE, log.p=FALSE) qt3(p, mean, sd, df, lower.tail=TRUE, log.p=FALSE) rt3(n, mean, sd, df)
x |
vector of parameter values |
location |
location of the t-distribution |
mean |
mean of the t-distribution |
scale |
scale parameter of the t-distribution |
sd |
standard deviation of the t-distribution, only defined for |
df |
degrees of freedom |
lower.tail |
logical; if TRUE (default), cumulative probabilities up to x, otherwise, above x. |
log.p |
logical; if TRUE, probabilities p are given as log(p). |
p |
probability. |
n |
number of random draws required. |
dtx
gives the density, ptx
gives the cumulative probability, qtx
gives the quantile function, and rtx
generates random deviates.
Mike Meredith
See the stats functions dt
, pt
, qt
, rt
.
## Plot the t-distribution with varying sd and scale require(graphics) xx <- seq(-5, 15, length=201) density <- dt3(xx, mean=5, sd=1, 4) plot(xx, density, type='l', lwd=2, main="t-distribution with df = 4") lines(xx, dt3(xx, 5, 2, 4), lwd=2, col=2) lines(xx, dt3(xx, 5, 3, 4), lwd=2, col=3) lines(xx, dt3(xx, 5, 4, 4), lwd=2, col=4) legend('topleft', paste0("sd = ", 1:4), lwd=2, lty=1, col=1:4, bty='n') lines(xx, dt2(xx, 5, 1, 4), lwd=2, lty=2, col=1) lines(xx, dt2(xx, 5, 2, 4), lwd=2, lty=2, col=2) lines(xx, dt2(xx, 5, 3, 4), lwd=2, lty=2, col=3) lines(xx, dt2(xx, 5, 4, 4), lwd=2, lty=2, col=4) legend('topright', paste0("scale = ", 1:4), lwd=2, lty=2, col=1:4, bty='n') # Generate random numbers rand2 <- rt2(1e6, location=5, scale=2, df=4) mean(rand2) sd(rand2) # about 2.83 rand3 <- rt3(1e6, mean=5, sd=2, df=4) mean(rand3) sd(rand3) # close to 2 # check pt* and qt* prob <- pt2(x=7, location=5, scale=3, df=4) qt2(p=prob, location=5, scale=3, df=4)
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