Overload List
| # | Signature | Description |
|---|---|---|
| 1 | procedure NormalCDF(const X: TDenseMtxVec; const Mu: TDenseMtxVec; const sigma: TDenseMtxVec; const Res: TDenseMtxVec); | Normal distribution CDF (vectorized). |
| 2 | procedure NormalCDF(const X: TDenseMtxVec; Mu: Double; sigma: Double; const Res: TDenseMtxVec); | Normal distribution CDF (vectorized). |
| 3 | function NormalCDF(x: Double; Mu: Double; sigma: Double): Double; | Normal (Gaussian) cumulative distribution function (CDF). |
Overload 1: procedure NormalCDF(const X: TDenseMtxVec; const Mu: TDenseMtxVec; const sigma: TDenseMtxVec; const Res: TDenseMtxVec);
Normal distribution CDF (vectorized).
| # | Name | Description |
|---|---|---|
| 1 | X | Defines distribution domain, real vector or matrix. |
| 2 | Mu | Distribution location parameter, real vector or matrix. |
| 3 | sigma | Distribution scale parameter, real positive vector or matrix. |
| 4 | Res | 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. |
Result: stored in self (calling object)
Overload 2: procedure NormalCDF(const X: TDenseMtxVec; Mu: Double; sigma: Double; const Res: TDenseMtxVec);
Normal distribution CDF (vectorized).
| # | Name | Description |
|---|---|---|
| 1 | X | Defines distribution domain, real vector or matrix. |
| 2 | Mu | Distribution location parameter, real value. |
| 3 | sigma | Distribution scale parameter, real positive value. |
| 4 | Res | 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. |
Result: stored in self (calling object)
Overload 3: function NormalCDF(x: Double; Mu: Double; sigma: Double): Double;
Normal (Gaussian) cumulative distribution function (CDF).
| # | Name | Description |
|---|---|---|
| 1 | x | Function domain, any real value. |
| 2 | Mu | Distribution location parameter (mean), any real value. |
| 3 | sigma | Distribution 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.
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 , is monotone non-decreasing, and tends to 0 as x -> -inf and to 1 as x -> +inf. If sigma <= 0 the result is NAN.