These functions provide information about the triangle distribution on the
interval from a to b with a maximum at c. dtriangle
gives the density, ptriangle gives the distribution function,
qtriangle gives the quantile function, and rtriangle generates
n random deviates.
number of observations. If length(n) > 1, the length
is taken to be the number required.
Details
All probabilities are lower tailed probabilities.
a, b, and c may be appropriate length vectors except in
the case of rtriangle.
rtriangle is derived from a draw from runif.
The triangle distribution has density:
f(x) = 2(x-a) / [(b-a)(c-a)]
for a <= x < c.
f(x) = 2(b-x) / [(b-a)(b-c)]
for c <= x <= b.
f(x) = 0 elsewhere.
The mean and variance are:
E(x) = (a + b + c) / 3
V(x) = (a^2 + b^2 + c^2 - ab - ac - bc) / 18
Value
dtriangle gives the density, ptriangle gives the distribution
function, qtriangle gives the quantile function, and rtriangle
generates random deviates.
Invalid arguments will result in return value NaN or NA.
Author(s)
Rob Carnell
References
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
The New S Language.
Wadsworth & Brooks/Cole.
See Also
.Random.seed about random number generation,
runif, etc for other distributions.