triangular: The Triangular Distribution

In SPLICE: Synthetic Paid Loss and Incurred Cost Experience (SPLICE) Simulator

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)

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.

Value

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

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)

SPLICE documentation built on May 29, 2024, 2:25 a.m.