Description Usage Arguments Value See Also Examples
cfX_Normal(t, mean, variance) evaluates the characteristic function cf(t) of the Normal distribution with mean = mean and variance = variance: N(mean, variance)) cfX_Normal(t, mean, variance) = exp(imeant -1/2variance^2t^2)
1 | cfX_Normal(t, mean = 0, variance = 1)
|
t |
numerical values (number, vector...) |
mean |
real number, mean or expextation of the distribution, default value mean = 0 |
variance |
real number, standard deviation, variance > 0, default value variance = 1 |
characteristic function cf(t) of the normal distribution
For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Normal_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_PearsonV
,
cfX_Rectangular
,
cfX_Triangular
1 2 3 4 5 6 7 8 9 10 11 | ## EXAMPLE1 (CF of the Normal distribution N(1,1))
t <- seq(-5, 5, length.out = 501)
plotGraf(function(t)
cfX_Normal(t, mean = 1, variance = 1), t, title = "CF of the Normal distribution N(1,1)")
## EXAMPLE2 (PDF/CDF of the Normal distribution N(1,1))
cf <- function(t)
cfX_Normal(t, mean = 1, variance = 1)
x <- seq(-4, 4, length.out = 101)
prob <- c(0.9, 0.95, 0.99)
result <- cf2DistGP(cf, x, prob, N = 2 ^ 5, SixSigmaRule = 8)
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