wiqid (version 0.3.3)

TDist: The Generalized Student's t Distribution

Description

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.

Usage

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)

Value

dtx gives the density, ptx gives the cumulative probability, qtx gives the quantile function, and rtx generates random deviates.

Arguments

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 > 2.

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.

Author

Mike Meredith

See Also

See the stats functions dt, pt, qt, rt.

Examples

## 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)