shape parameter $\theta$. Parameter estimation can be based on a weighted or unweighted i.i.d. sample
and can be performed numerically.
dTriangular(x, a = 0, b = 1, theta = 0.5, params = list(a, b, theta), ...)
pTriangular(q, a = 0, b = 1, theta = 0.5, params = list(a, b, theta), ...)
qTriangular(p, a = 0, b = 1, theta = 0.5, params = list(a, b, theta), ...)
rTriangular(n, a = 0, b = 1, theta = 0.5, params = list(a, b, theta), ...)
eTriangular(X, w, method = "numerical.MLE", ...)
lTriangular(X, w, a = 0, b = 1, theta = 0.5, params = list(a, b, theta), logL = TRUE, ...)a, b or theta are not specified they assume the default values of 0, 1 and 0.5 respectively.The dTriangle(), pTriangle(), qTriangle(),and rTriangle() functions serve as wrappers of the
dtriangle, ptriangle, qtriangle, and
rtriangle functions in the VGAM package. They allow for the parameters to be declared not only as
individual numerical values, but also as a list so parameter estimation can be carried out.
The triangular distribution has a probability density function, defined in Forbes et.al (2010), that consists of two lines joined at $theta$, where $theta$ is the location of the mode.
Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2010) Triangular Distribution, in Statistical Distributions, Fourth Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA.