# dtri: The triangular distribution. In metRology: Support for Metrological Applications

## Description

Density, distribution function, quantile function and random generation for the triangular distribution with range 'min' to 'max' and mode equal to 'mode'.

## Usage

  1 2 3 4 5 6 7 8 9 10 dtri(x, min=-sqrt(6), max=sqrt(6), mode = (min + max)/2, log = FALSE) ptri(q, min=-sqrt(6), max=sqrt(6), mode = (min + max)/2, lower.tail = TRUE, log.p = FALSE) qtri(p, min=-sqrt(6), max=sqrt(6), mode = (min + max)/2, lower.tail = TRUE, log.p = FALSE) rtri(n, min=-sqrt(6), max=sqrt(6), mode = (min + max)/2) 

## Arguments

 x, q Vector of quantiles. p Vector of quantiles. n Number of observations. If 'length(n) > 1', the length is taken to be the number required. min Vector of lower limits of distribution. max Vector of upper limits of distribution. mode Vector of modes 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

The triangular distribution has density

f(x)=2*(x-min) / ((max-min)*(mode-min)) (min < x <= mode)

f(x)=2*(max-x) / ((max-min)*(max-mode)) (mode < x < max)

and 0 elsewhere.

The mean is

(min + mode + max)/3

and the variance is

\frac{1}{18}(min^2 + mode^2 + max^2 - min*mode - min*max - mode*max)

The default values of min, max and mode give a distribution with mean 0 and unit variance.

If min>max, min amd max will be silently interchanged. If mode is not within [min, max], the functions return NA, with a warning.

rtri calls runif(n, 0, 1) to generate probabilities which are passed to qtri.

## Value

A vector of densities, probabilities, quantiles or random deviates. dtri gives the density, ptri gives the distribution function, qtri gives the quantile function, and rtri generates random deviates.

## Author(s)

S. L. R. Ellison s.ellison@lgc.co.uk

runif
  1 2 3 4 5 6 7 8 9 10 ` require(graphics) x<-seq(-3,3,0.02) par(mfrow=c(2,1)) plot(x, dtri(x), type="l", main="Density") plot(x, ptri(x), type="l", main="p(X