Functions to compute the probability density function, cumulative distribution function, and quantile function for the Triangular distribution.
The triangular distribution is a continuous probability distribution with a lower limit \(a\), mode \(c\), and upper limit \(b\). It is often used where the distribution is only vaguely known, but upper and lower limits are known, and a "best guess" (mode) is added.
It has the probability density function (PDF): $$f(x) = \frac{2(x-a)}{(b-a)(c-a)} \quad \text{for } a \le x \le c$$ $$f(x) = \frac{2(b-x)}{(b-a)(b-c)} \quad \text{for } c < x \le b$$
Accuracy and Implementation Notes: The triangular distribution is implemented with simple arithmetic operators and so should have errors within an epsilon or two.
Usage
triangular_distribution(lower = -1, mode = 0, upper = 1)
triangular_pdf(x, lower = -1, mode = 0, upper = 1)
triangular_lpdf(x, lower = -1, mode = 0, upper = 1)
triangular_cdf(x, lower = -1, mode = 0, upper = 1)
triangular_lcdf(x, lower = -1, mode = 0, upper = 1)
triangular_quantile(p, lower = -1, mode = 0, upper = 1)Value
A single numeric value with the computed probability density, log-probability density, cumulative distribution, log-cumulative distribution, or quantile depending on the function called.
See also
Boost Documentation for more details on the mathematical background.
Examples
# Triangular distribution with lower = -1, mode = 0, upper = 1
dist <- triangular_distribution(-1, 0, 1)
# Apply generic functions
cdf(dist, 0.5)
#> [1] 0.875
logcdf(dist, 0.5)
#> [1] -0.1335314
pdf(dist, 0.5)
#> [1] 0.5
logpdf(dist, 0.5)
#> [1] -0.6931472
hazard(dist, 0.5)
#> [1] 4
chf(dist, 0.5)
#> [1] 2.079442
mean(dist)
#> [1] 0
median(dist)
#> [1] 0
mode(dist)
#> [1] 0
range(dist)
#> [1] -1.797693e+308 1.797693e+308
quantile(dist, 0.2)
#> [1] -0.3675445
standard_deviation(dist)
#> [1] 0.4082483
support(dist)
#> [1] -1 1
variance(dist)
#> [1] 0.1666667
skewness(dist)
#> [1] 0
kurtosis(dist)
#> [1] 2.4
kurtosis_excess(dist)
#> [1] -0.6
# Convenience functions
triangular_pdf(1)
#> [1] 0
triangular_lpdf(1)
#> [1] -Inf
triangular_cdf(1)
#> [1] 1
triangular_lcdf(1)
#> [1] 0
triangular_quantile(0.5)
#> [1] 0