dst {lazy.stat}

R Documentation

t distribution

Description

t distribution

Usage

dst(x, df, m = 0, c2 = 1, sd = 0)

pst(x, df, m = 0, c2 = 1, sd = 0)

qst(p, df, m = 0, c2 = 1, sd = 0)

Arguments

x,	q vector of quantiles.
df	The degrees of freedom
m	The mean
c2	The scale parameter or NULL
sd	The standard deviation: This has priority over c2.
p	vector of probabilities.
n	# of random numbers to be generated.

Details

X ~ t( df, m, c2 ) means that
(X-m) / sqrt(c2) ~ t( df, m=0, c2=1 )

If Y ~ t( df ) then Y * sqrt(c2) + m ~ t( df, m, c2 )

variance of t( df, m=0, c2=1 ) = df/(df-2)
variance of t( df, m, c2 ) = c2 * df/(df-2)

Value

rst returns the vector of length n.
Other functions return the vector of length length(x) or length(p)

Examples

df <- 10
m <- 1
c2 <- 4
var <- df/(df-2)*c2
x <- seq(-4,6,length.out=31)

pdft <- dst( x, df, m, c2 )
pdfn <- dnorm( x, m, sqrt(var) )
matplot(x, cbind(pdft,pdfn), type <- "l")

pn <- pnorm( x, m, sqrt(var) )
p <- pst( x, df, m, c2 )
q <- qst( p, df, m, c2 )
Print( x, pn, p, q )

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