Description Usage Arguments Value See Also Examples
cfS_Trapezoidal(t, a, c) (a > 0, c > 0, c ≤ a) evaluates the characteristic function cf(t) of the Trapezoidal distribution on the interval (-a, a) with mode on the interval (-c, c) (Trapezoidal distribution with mean = 0 and variance = ??? cfS_Trapezoidal(t, a, c) = (sin(w*at)/(w*at))*(sin((1-w)*at)/((1-w)*at))
1 | cfS_Trapezoidal(t, a = 1, c = 1/3)
|
t |
numerical values (number, vector...) |
a |
number, a > 0, default value a = 1 |
c |
number, (0 ≤ c ≤ a), default value c = 1/3 |
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/Trapezoidal_distribution
Other Continuous Probability distribution: cfS_Arcsine
,
cfS_Beta
, cfS_Gaussian
,
cfS_Rectangular
,
cfS_StudentT
, cfS_Triangular
,
cfX_Beta
, cfX_ChiSquared
,
cfX_Exponential
, cfX_Gamma
,
cfX_InverseGamma
,
cfX_LogNormal
, cfX_Normal
,
cfX_PearsonV
,
cfX_Rectangular
,
cfX_Triangular
Other Symetric Probability distribution: cfS_Arcsine
,
cfS_Gaussian
,
cfS_Rectangular
,
cfS_StudentT
, cfS_Triangular
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ## EXAMPLE1 (CF of the Trapezoidal distribution with a = 1, c = 0.5)
t <- seq(-15, 15, length.out = 501)
plotGraf(function(t)
cfS_Trapezoidal(t, c = 1 / 2), t,
title = "CF of the Trapezoidal distribution with a = 1, c = 0.5")
## EXAMPLE2 (PDF/CDF of the compound Trapezoidal distribution with a = 1, c = 0.5)
cf <- function(t)
cfS_Trapezoidal(t, c = 1 / 2)
x <- seq(-1, 1, length.out = 100)
prob <- c(0.9, 0.95, 0.99)
xRange <- 2
option <- list()
option$N <- 1000
option$dx <- 2 / pi / xRange
result <- cf2DistGP(cf, x, option = option)
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