triangle | R Documentation |
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)
x, q |
vector of quantiles. |
a |
lower limit of the distribution. |
b |
upper limit of the distribution. |
c |
mode of the distribution. |
p |
vector of probabilities. |
n |
number of observations. If |
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
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
.
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 var(tri) # 1/18*(1^2 + 3^2 + 5^2 - 1*5 - 1*3 - 5*3) = 0.666667 dtriangle(0.5, 0, 1, 0.5) # 2/(b-a) = 2 qtriangle(ptriangle(0.7)) # 0.7
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