Description Usage Arguments Value See Also Examples
cfX_Triangular(t, a, b, c) (a ≤ c ≤ b) evaluates the characteristic function cf(t) of the Triangular distribution on the interval (a, b) with mode c (Triangular distribution with mean = a + b + c)/3 and variance = 1/18(a^2 + b^2 + c^2 + - ab - ac - bc)) cfX_Triangula(t, a, b, c) = -2((b-c)exp(iat) - (b-a)exp(ict) + (c-a)exp(ibt))/((b-a)(c-a)(b-c)t^2)
1 | cfX_Triangular(t, a = -1, b = 1, c = 0)
|
t |
numerical values (number, vector...) |
a |
number, default value a = -1 |
b |
number, default value b = 1 |
c |
number, (a ≤ c ≤ b), default value c = 0 |
characteristic function cf(t) of the Triangular distribution on the interval (a, b) with mode c
For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Triangular_distribution
Other Continuous Probability distribution: cfS_Arcsine
,
cfS_Beta
, cfS_Gaussian
,
cfS_Rectangular
,
cfS_StudentT
,
cfS_Trapezoidal
,
cfS_Triangular
, cfX_Beta
,
cfX_ChiSquared
,
cfX_Exponential
, cfX_Gamma
,
cfX_InverseGamma
,
cfX_LogNormal
, cfX_Normal
,
cfX_PearsonV
, cfX_Rectangular
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ## EXAMPLE1 (CF of the Triangular distribution on (-1 , 2) mode = 0)
t <- seq(-10, 10, length.out = 501)
plotGraf(function(t)
cfX_Triangular(t, a = -1, b = 2, c = 0), t,
title = "CF of the Triangular distribution on (-1 , 2)")
## EXAMPLE2 (PDF/CDF of the Triangular distribution on (-1 , 2) mode = 0)
cf <- function(t)
cfX_Triangular(t, a = -1, b = 2, c = 0)
x <- seq(-1, 2, length.out = 101)
prob <- c(0.9, 0.95, 0.99)
xRange <- 3
option <- list()
option$N <- 2 ^ 10
option$dx <- 2 / pi / xRange
result <- cf2DistGP(cf, x, option = option)
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