Triangular {extraDistr} | R Documentation |
Triangular distribution
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 |
vector of probabilities. |
n |
number of observations. If |
Details
Probability density function
Cumulative distribution function
Quantile function
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)