Scaled t distribution {metRology}

Scaled and shifted t distribution.

Description

Student's t distribution for 'df' degrees of freedom, shifted by 'mean' and scaled by 'sd'.

Usage

dt.scaled(x, df, mean = 0, sd = 1, ncp, log = FALSE)
pt.scaled(q, df, mean = 0, sd = 1, ncp, lower.tail = TRUE, log.p = FALSE)
qt.scaled(p, df, mean = 0, sd = 1, ncp, lower.tail = TRUE, log.p = FALSE)
rt.scaled(n, df, mean = 0, sd = 1, ncp)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

df

degrees of freedom (> 0, maybe non-integer). df = Inf is allowed.

mean

mean value for the shifted, scaled distribution.

sd

Scale factor for the shifted, scaled distribution.

ncp

non-centrality parameter delta; currently except for rt(), only for abs(ncp) <= 37.62. If omitted, use the central t distribution.

lower.tail

logical; if TRUE (default), probabilities are P[X <= x]; otherwise, P[X > x].

log, log.p

logical; if TRUE, probabilities p are given as log(p).

Details

These are wrappers for the corresponding t distribution functions in package stats.

The scaled, shifted t distribution has mean mean and variance sd^2 * df/(df-2)

The scaled, shifted t distribution is used for Monte Carlo evaluation when a value x has been assigned a standard uncertainty u associated with with df degrees of freedom; the corresponding distribution function for that is then t.scaled with mean=x, sd=u and df=df.

Value

dt.scaled gives the density, pt.scaled gives the distribution function, qt.scaled gives the quantile function, and rt.scaled generates random deviates.

Invalid arguments will result in return value NaN, with a warning.

Author(s)

S. L. R. Ellison [e-mail]

See Also

TDist

Examples

	u<-rt.scaled(20, df=5, mean=11, sd=0.7)
	
	qt.scaled(c(0.025,0.975), Inf, mean=10, sd=1) #10 +- 1.96*sd
	
	require(graphics)
	hist(rt.scaled(10000, df=4, mean=11, sd=0.7), breaks=50, probability=TRUE)
	x<-seq(0,25, 0.05)
	lines(x,dnorm(x,mean=11, sd=0.7), col=2)