cfX_Normal: Characteristic function of Normal distribution

In CharFun: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

Description

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)

Usage

cfX_Normal(t, mean = 0, variance = 1)

Arguments

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

Value

characteristic function cf(t) of the normal distribution

See Also

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

Examples

## 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)

CharFun documentation built on May 2, 2019, 9:18 a.m.