Triangular: Triangular distribution

In extraDistr: Additional Univariate and Multivariate Distributions

Description

Density, distribution function, quantile function and random generation for the triangular distribution.

Usage

dtriang(x, a = -1, b = 1, c = (a + b)/2, log = FALSE)

ptriang(q, a = -1, b = 1, c = (a + b)/2, lower.tail = TRUE, log.p = FALSE)

qtriang(p, a = -1, b = 1, c = (a + b)/2, lower.tail = TRUE, log.p = FALSE)

rtriang(n, a = -1, b = 1, c = (a + b)/2)

Arguments

x, q	vector of quantiles.
a, b, c	minimum, maximum and mode of the distribution.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x].
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

Probability density function

f(x) = [if x < c:] (2*(x-a)) / ((b-a)*(c-a)) [if x = c:] 2/(b-a) [if x >= c:] (2*(b-x)) / ((b-a)*(b-c))

Cumulative distribution function

F(x) = [if x <= c:] (x-a)^2 / ((b-a)*(c-a)) [if x > c:] 1 - ((b-x)^2 / ((b-a)*(b-c)))

Quantile function

F^-1(p) = [if p < (c-a)/(b-a):] a + sqrt(p*(b-a)*(c-a)) [else:] b - sqrt((1-p)*(b-a)*(b-c))

For random generation MINMAX method described by Stein and Keblis (2009) is used.

References

Forbes, C., Evans, M. Hastings, N., & Peacock, B. (2011). Statistical Distributions. John Wiley & Sons.

Stein, W. E., & Keblis, M. F. (2009). A new method to simulate the triangular distribution. Mathematical and computer modelling, 49(5), 1143-1147.

Examples

x <- rtriang(1e5, 5, 7, 6)
hist(x, 100, freq = FALSE)
curve(dtriang(x, 5, 7, 6), 3, 10, n = 500, col = "red", add = TRUE)
hist(ptriang(x, 5, 7, 6))
plot(ecdf(x))
curve(ptriang(x, 5, 7, 6), 3, 10, n = 500, col = "red", lwd = 2, add = TRUE)

extraDistr documentation built on Sept. 7, 2020, 5:09 p.m.