Probabilities.NormalCDF Method

Overload List

#SignatureDescription
1void NormalCDF(TDenseMtxVec X, TDenseMtxVec Mu, TDenseMtxVec sigma, TDenseMtxVec Res)Normal distribution CDF (vectorized).
2void NormalCDF(TDenseMtxVec X, Double Mu, Double sigma, TDenseMtxVec Res)Normal distribution CDF (vectorized).
3Double NormalCDF(Double x, Double Mu, Double sigma)Normal (Gaussian) cumulative distribution function (CDF).

Overload 1: void NormalCDF(TDenseMtxVec X, TDenseMtxVec Mu, TDenseMtxVec sigma, TDenseMtxVec Res)

Normal distribution CDF (vectorized).

#NameDescription
1XDefines distribution domain, real vector or matrix.
2MuDistribution location parameter, real vector or matrix.
3sigmaDistribution scale parameter, real positive vector or matrix.
4ResAfter calculation stores the CDF calculated from X, mi and sigma. Length and Complex properties of Res are adjusted automatically to match Length and Complex properties of X.

Result: stored in self (calling object)

Overload 2: void NormalCDF(TDenseMtxVec X, Double Mu, Double sigma, TDenseMtxVec Res)

Normal distribution CDF (vectorized).

#NameDescription
1XDefines distribution domain, real vector or matrix.
2MuDistribution location parameter, real value.
3sigmaDistribution scale parameter, real positive value.
4ResAfter calculation stores the CDF calculated from X, mi and sigma. Length and Complex properties of Res are adjusted automatically to match Length and Complex properties of X.

Result: stored in self (calling object)

Overload 3: Double NormalCDF(Double x, Double Mu, Double sigma)

Normal (Gaussian) cumulative distribution function (CDF).

#NameDescription
1xFunction domain, any real value.
2MuDistribution location parameter (mean), any real value.
3sigmaDistribution scale parameter (standard deviation), real value > 0.

Returns: Double - the normal cumulative distribution function (CDF) at x for mean Mu and standard deviation sigma; the probability that an observation falls in (-INF, x]. Returns NAN when sigma <= 0.

Remarks:

Computes the normal CDF

CDF(x| mu,sigma )= 1/(sigma sqrt(2pi))integral _(-inf) ^x exp ( - ((t-mu)^2)/(2sigma ^2)) dt = 1/2[1+erf((x-mu)/sigmasqrt(2))]

(the implementation uses the error-function closed form, clamped to at most 1). Domain: x in R, mu in R, sigma > 0; the result lies in [0,1][0,1], is monotone non-decreasing, and tends to 0 as x -> -inf and to 1 as x -> +inf. If sigma <= 0 the result is NAN.

See Also: Probabilities.NormalPDF, Probabilities.NormalCDFInv