Probabilities::NormalCDF Function

Probabilities Namespace

Overload List

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

Overload 1: double NormalCDF(double x, double Mu, double sigma);

Normal (Gaussian) cumulative distribution function (CDF).

#NameTypeDescription
1xdoubleFunction domain, any real value.
2MudoubleDistribution location parameter (mean), any real value.
3sigmadoubleDistribution scale parameter (standard deviation), real value > 0.

Returns: 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
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler

Overload 2: void NormalCDF(TDenseMtxVec *X, double Mu, double sigma, TDenseMtxVec *Res);

Normal distribution CDF (vectorized).

#NameTypeDescription
1XTDenseMtxVec *Defines distribution domain, real vector or matrix.
2MudoubleDistribution location parameter, real value.
3sigmadoubleDistribution scale parameter, real positive value.
4ResTDenseMtxVec *After 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.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler

Overload 3: void NormalCDF(TDenseMtxVec *X, TDenseMtxVec *Mu, TDenseMtxVec *sigma, TDenseMtxVec *Res);

Normal distribution CDF (vectorized).

#NameTypeDescription
1XTDenseMtxVec *Defines distribution domain, real vector or matrix.
2MuTDenseMtxVec *Distribution location parameter, real vector or matrix.
3sigmaTDenseMtxVec *Distribution scale parameter, real positive vector or matrix.
4ResTDenseMtxVec *After 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.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler