Description Usage Arguments Value See Also Examples
cfX_ChiSquared(t, df, ncp = 0) evaluates the characteristic function cf(t) of the Chi-Squared distribution with the parameter df (degrees of freedom, df > 0) and npc (non-centrality, npc ≥ 0), i.e.
cfX_ChiSquared(t, df, npc) = exp((i*npc*t)/(1 - 2it)) / (1 - 2it)^(df/2)
1 | cfX_ChiSquared(t, df, npc = 0)
|
t |
numerical values (number, vector...) |
df |
degrees of freedom |
npc |
non-centrality parameter, default value = 0 |
characteristic function cf(t) of the CHI-SUQARED distribution
For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution
Other Continuous Probability distribution: cfS_Arcsine
,
cfS_Beta
, cfS_Gaussian
,
cfS_Rectangular
,
cfS_StudentT
,
cfS_Trapezoidal
,
cfS_Triangular
, cfX_Beta
,
cfX_Exponential
, cfX_Gamma
,
cfX_InverseGamma
,
cfX_LogNormal
, cfX_Normal
,
cfX_PearsonV
,
cfX_Rectangular
,
cfX_Triangular
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 | ## EXAMPLE1 (CF of the ChiSquared distribution with df = 1)
df <- 1
t <- seq(-50, 50, length.out = 501)
plotGraf(function(t)
cfX_ChiSquared(t, df), t, title = "CF of the Chi-squared distribution with df = 1")
## EXAMPLE2 (PDF/CDF of the ChiSquared distribution with df = 3)
df <- 3
prob <- c(0.9, 0.95, 0.99)
cf <- function(t)
cfX_ChiSquared(t, df)
x <- seq(-0, 15, length.out = 101)
result <- cf2DistGP(cf,
x,
prob,
xMin = 0,
xMax = 22,
N = 2 ^ 14)
## EXAMPLE3 (PDF/CDF of the compound Binomial-ChiSquared distribution)
n <- 25
p <- 0.3
df <- 3
prob <- c(0.9, 0.95, 0.99)
cfX <- function(t)
cfX_ChiSquared(t, df)
cf <- function(t)
cfN_Binomial(t, n, p, cfX)
x <- seq(-0, 80, length.out = 501)
result <- cf2DistGP(cf, x, prob, isCompound = TRUE)
## EXAMPLE4 (CF of the ChiSquared distribution with df = 1, npc = 2)
df <- 1
npc <- 2
t <- seq(-50, 50, length.out = 501)
plotGraf(function(t)
cfX_ChiSquared(t, df, npc), t, title = "CF of the Chi-squared distribution with df = 1, npc = 2")
## EXAMPLE5 (PDF/CDF of the ChiSquared distribution with df = 3, npc = 2)
df <- 3
npc <- 2
prob <- c(0.9, 0.95, 0.99)
cf <- function(t)
cfX_ChiSquared(t, df, npc)
x <- seq(-0, 15, length.out = 101)
result <- cf2DistGP(cf, x, prob, N = 2 ^ 14)
## EXAMPLE6 (PDF/CDF of the compound Binomial-ChiSquared distribution)
n <- 25
p <- 0.3
df <- 3
npc <- 2
prob <- c(0.9, 0.95, 0.99)
cfX <- function(t)
cfX_ChiSquared(t, df, npc)
cf <- function(t)
cfN_Binomial(t, n, p, cfX)
x <- seq(-0, 80, length.out = 501)
result <- cf2DistGP(cf, x, prob, isCompound = TRUE)
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