Summary
Normal probability density function (PDF).Unit
Probabilities
Declaration
Procedure NormalPDF(X: TDenseMtxVec; Mu, Sigma: TSample; Res: TDenseMtxVec);
Description
Calculates the normal PDF for vector X using the parameters Mu and Sigma. The results are stored in vector Res. The Res Length and Complex properties are adjusted automatically. If vector X is complex, an exception is raised.Declaration
Function NormalPDF(x: TSample; mu, sigma: TSample): TSample;
Result
the normal probability density function (PDF) for value x using the parameters mu (mean value) and sigma (standard deviation). Sigma must be positive value, otherwise the result is NAN. The normal probability density function is defined by the following equation:
where m (mu) is mean value and s is standard deviation (sigma). Special case of normal distribution (mean = 0, sigma =1) is called standard normal distribution.
The normal distribution is a distribution that underlies many of the statistical methods used in data analysis. This distribution is often referred to as "Gaussian" distribution. Normal distribution can be used for modeling when the sample size is large. The theoretical justification can be found in Central Limit Theorem which states (roughly) that the sum of independent samples from any distribution with finite mean and variance converges to the normal distribution as the sample size goes to infinity.
Categories
Continuous probabilities| See Also |
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| NormalCDF |
| NormalCDFInv |
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