Normal Distribution

Generates normally distributed random numbers.

Details

Normal (Gaussian) random number generator fills the input n x p numeric table with Gaussian random numbers with mean α and standard deviation σ, where α, σ∈R and σ > 0. The probability density function is given by:

\[f_{\alpha, \sigma}(x) = \frac {1}{\sigma \sqrt{2\pi}}\exp(-\frac {(x - a)^2}{2\sigma^2}), -\infty < x < +\infty\]

The cumulative distribution function is as follows:

\[F_{\alpha, \sigma}(x) = \int _{-\infty}^{x} \frac {1}{\sigma \sqrt{2\pi}} \exp(-\frac {(y - a)^2}{2\sigma^2})dy, -\infty < x < +\infty\]

Batch Processing

Algorithm Parameters

Normal distribution algorithm has the following parameters in addition to the common parameters specified in Distributions:

Parameter

Default Value

Description

algorithmFPType

float

The floating-point type that the algorithm uses for intermediate computations. Can be float or double.

method

defaultDense

Performance-oriented computation method, the only method supported by the algorithm. The only method supported so far is the Inverse Cumulative Distribution Function (ICDF) method.

a

\(0\)

The mean \(\alpha\)

sigma

\(1\)

The standard deviation \(\sigma\)

Examples

Batch Processing: