The Triangle Distribution

Density, distribution function, quantile function and random generation for the Triangle distribution with parameter theta.

dtriangle(x, theta, lower = 0, upper = 1, log = FALSE)
ptriangle(q, theta, lower = 0, upper = 1, lower.tail = TRUE, log.p = FALSE)
qtriangle(p, theta, lower = 0, upper = 1, lower.tail = TRUE, log.p = FALSE)
rtriangle(n, theta, lower = 0, upper = 1)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. Same as runif.

theta

the theta parameter which lies between lower and upper.

lower, upper

lower and upper limits of the distribution. Must be finite.

log

Logical. If log = TRUE then the logarithm of the density is returned.

lower.tail, log.p

Same meaning as in pnorm or qnorm.

Value

dtriangle gives the density, ptriangle gives the distribution function, qtriangle gives the quantile function, and rtriangle generates random deviates.

Author

T. W. Yee and Kai Huang

Details

See triangle, the VGAM family function for estimating the parameter \(\theta\) by maximum likelihood estimation, however the regular conditions do not hold so the algorithm crawls to the solution if lucky.

See also

triangle, topple.

Examples

if (FALSE)  x <- seq(-0.1, 1.1, by = 0.01); theta <- 0.75
plot(x, dtriangle(x, theta = theta), type = "l", col = "blue", las = 1,
     main = "Blue is density, orange is the CDF",
     sub = "Purple lines are the 10,20,...,90 percentiles",
     ylim = c(0,2), ylab = "")
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'x' not found
abline(h = 0, col = "blue", lty = 2)
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet
lines(x, ptriangle(x, theta = theta), col = "orange")
#> Error: object 'x' not found
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qtriangle(probs, theta = theta)
lines(Q, dtriangle(Q, theta = theta), col = "purple", lty = 3, type = "h")
#> Error in plot.xy(xy.coords(x, y), type = type, ...): plot.new has not been called yet
ptriangle(Q, theta = theta) - probs  # Should be all zero
#> [1]  2.775558e-17  2.775558e-17  0.000000e+00  1.110223e-16 -5.551115e-17
#> [6]  0.000000e+00  0.000000e+00  0.000000e+00 -1.110223e-16
abline(h = probs, col = "purple", lty = 3)  # \dontrun{}
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet