SPLICE (version 1.1.2)

triangular: The Triangular Distribution

Description

Density, distribution function, quantile function and random generation for the triangular distribution with parameters min, max and mode.

Usage

ptri(q, min, max, mode)
dtri(x, min, max, mode)
qtri(p, min, max, mode)
rtri(n, min, max, mode)

Value

dtri gives the density, ptri gives the distribution function, qtri gives the quantile function, and rtri generates random deviates.

Arguments

min

vector of minimum values.

max

vector of maximum values.

mode

vector of modes.

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.

Details

The triangular distribution with parameters min\(= a\), max \(= b\), mode\(= c\) has density:

\(f(x) =\)	\(\frac{2(x-a)}{(b-a)(c-a)}\)	for \(a < x \le c\)
	\(\frac{2(b-x)}{(b-a)(b-c)}\)	for \(c < x \le b\)
	\(0\)	otherwise

and distribution function:

\(F(x) =\)	\(0\)	for \(x \le a\)
	\(\frac{(x-a)^2}{(b-a)(c-a)}\)	for \(a < x \le c\)
	\(1 - \frac{(b-x)^2}{(b-a)(b-c)}\)	for \(c < x \le b\)
	\(1\)	for \(x > b\)

for \(a \le c \le b\).

Examples

ptri(c(0, 1/2, 1), min = 0, max = 1, mode = 1/2)
dtri(c(0, 1/2, 1), min = 0, max = 1, mode = 1/2)
plot(function(x) dtri(x, min = 0, max = 1, mode = 1/2), 0, 1)