Probabilities.NormalCDFTwoTail Method

Overload List

#SignatureDescription
1procedure NormalCDFTwoTail(const X: TDenseMtxVec; const Mu: TDenseMtxVec; const sigma: TDenseMtxVec; const Res: TDenseMtxVec);Normal distribution two-tailed probability (vectorized; vector or matrix Mu, sigma).
2procedure NormalCDFTwoTail(const X: TDenseMtxVec; const Mu: Double; const sigma: Double; const Res: TDenseMtxVec);Normal distribution two-tailed probability (vectorized; scalar Mu, sigma).

Overload 1: procedure NormalCDFTwoTail(const X: TDenseMtxVec; const Mu: TDenseMtxVec; const sigma: TDenseMtxVec; const Res: TDenseMtxVec);

Normal distribution two-tailed probability (vectorized; vector or matrix Mu, sigma).

#NameDescription
1XDistribution domain, real vector or matrix.
2MuDistribution location parameter, real vector or matrix (elementwise).
3sigmaDistribution scale parameter, real positive vector or matrix (elementwise).
4ResAfter calculation stores the two-tail probability computed from X, Mu 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)

Returns: For each element, the upper two-tail probability of the normal distribution, P(|Z| > |x-mu|/sigma) = 1 - erfbigl(|x-mu|/(sigmasqrt(2))bigr). Elements with the corresponding sigma<=0 are not guarded and divide by zero; supply sigma>0.

Remarks:

Computes elementwise the upper (symmetric) two-tail normal probability

Res = 1 - erf((|x-mu|)/sigmasqrt(2)) = 2(1-Phi((|x-mu|)/sigma)) ,

i.e. the probability that a standard normal deviate falls outside +/-|x-mu|/sigma. The value is 1 at x=mu and decreases toward 0 as |x-mu| grows.

See Also: Probabilities.NormalCDF

Overload 2: procedure NormalCDFTwoTail(const X: TDenseMtxVec; const Mu: Double; const sigma: Double; const Res: TDenseMtxVec);

Normal distribution two-tailed probability (vectorized; scalar Mu, sigma).

#NameDescription
1XDistribution domain, real vector or matrix.
2MuDistribution location parameter, real value.
3sigmaDistribution scale parameter, real positive value (sigma>0).
4ResAfter calculation stores the two-tail probability computed from X, Mu 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)

Returns: For each element of X, the upper two-tail probability of the normal distribution, P(|Z| > |x-mu|/sigma) = 1 - erfbigl(|x-mu|/(sigmasqrt(2))bigr). If sigma<=0 every element of Res is set to NaN.

Remarks:

Computes elementwise the upper (symmetric) two-tail normal probability

Res = 1 - erf((|x-mu|)/sigmasqrt(2)) = 2(1-Phi((|x-mu|)/sigma)) ,

i.e. the probability that a standard normal deviate falls outside +/-|x-mu|/sigma. The value is 1 at x=mu and decreases toward 0 as |x-mu| grows. If sigma<=0 the result is NaN.

See Also: Probabilities.NormalCDF