dtri: The triangular distribution.

In metRology: Support for Metrological Applications

The triangular distribution.

Description

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

Usage

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

\frac{1}{3}(min + mode + max)

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 [e-mail]

See Also

runif

Examples

     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<x)")

     u <- rtri(5000)

     var(rtri(10000,-1,1))  # ~ = 1/6 = 0.167

metRology documentation built on Dec. 16, 2024, 3:01 a.m.