metRology (version 0.9-28-1)

Triangular: 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)

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.

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).

Author

S. L. R. Ellison

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.

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