# dt.scaled: Scaled and shifted t distribution. In metRology: Support for Metrological Applications

## Description

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

## Usage

 ```1 2 3 4``` ```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 [email protected]

`TDist`
 ```1 2 3 4 5 6 7 8``` ``` 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) ```