R/dtriangle.R
, R/ptriangle.r
, R/qtriangle.R
, and 1 more
triangle.Rd
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.
dtriangle(x, a = 0, b = 1, c = (a + b)/2)
ptriangle(q, a = 0, b = 1, c = (a + b)/2)
qtriangle(p, a = 0, b = 1, c = (a + b)/2)
rtriangle(n = 1, a = 0, b = 1, c = (a + b)/2)
vector of quantiles.
lower limit of the distribution.
upper limit of the distribution.
mode of the distribution.
vector of probabilities.
number of observations. If length(n) > 1
, the length is taken to be the number required.
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
.
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:
$$f(x) = \frac{2(x-a)}{(b-a)(c-a)}$$
for \(a \le x < c\).
$$f(x) = \frac{2(b-x)}{(b-a)(b-c)}$$
for \(c \le x \le b\).
\(f(x) = 0\) elsewhere.
The mean and variance are:
$$E(x) = \frac{(a + b + c)}{3}$$
$$V(x) = \frac{1}{18}(a^2 + b^2 + c^2 - ab - ac - bc)$$
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
.Random.seed
about random number generation,
runif
, etc for other distributions.
## view the distribution
tri <- rtriangle(100000, 1, 5, 3)
hist(tri, breaks=100, main="Triangle Distribution", xlab="x")
mean(tri) # 1/3*(1 + 5 + 3) = 3
#> [1] 3.002188
var(tri) # 1/18*(1^2 + 3^2 + 5^2 - 1*5 - 1*3 - 5*3) = 0.666667
#> [1] 0.6679719
dtriangle(0.5, 0, 1, 0.5) # 2/(b-a) = 2
#> [1] 2
qtriangle(ptriangle(0.7)) # 0.7
#> [1] 0.7