# Triangular: Triangular distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```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

 ```1 2 3 4 5 6``` ```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.