Parallel Colt 0.10.1
cern.jet.random.tdouble

## Class Normal

• All Implemented Interfaces:
DoubleFunction, IntFunction, Serializable, Cloneable

```public class Normal
extends AbstractContinousDoubleDistribution```
Normal (aka Gaussian) distribution; See the math definition and animated definition.
```
1                       2
pdf(x) = ---------    exp( - (x-mean) / 2v )
sqrt(2pi*v)

x
-
1        | |                 2
cdf(x) = ---------    |    exp( - (t-mean) / 2v ) dt
sqrt(2pi*v)| |
-
-inf.
```
where v = variance = standardDeviation^2.

Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.

Static methods operate on a default uniform random number generator; they are synchronized.

Implementation: Polar Box-Muller transformation. See G.E.P. Box, M.E. Muller (1958): A note on the generation of random normal deviates, Annals Math. Statist. 29, 610-611.

Version:
1.0, 09/24/99
Author:
wolfgang.hoschek@cern.ch
Serialized Form
• ### Constructor Summary

Constructors
Constructor and Description
```Normal(double mean, double standardDeviation, DoubleRandomEngine randomGenerator)```
Constructs a normal (gauss) distribution.
• ### Method Summary

Methods
Modifier and Type Method and Description
`double` `cdf(double x)`
Returns the cumulative distribution function.
`double` `nextDouble()`
Returns a random number from the distribution.
`double` ```nextDouble(double mean, double standardDeviation)```
Returns a random number from the distribution; bypasses the internal state.
`double` `pdf(double x)`
Returns the probability distribution function.
`void` ```setState(double mean, double standardDeviation)```
Sets the mean and variance.
`static double` ```staticNextDouble(double mean, double standardDeviation)```
Returns a random number from the distribution with the given mean and standard deviation.
`String` `toString()`
Returns a String representation of the receiver.
• ### Methods inherited from class cern.jet.random.tdouble.AbstractDoubleDistribution

`apply, apply, clone, makeDefaultGenerator, nextInt`
• ### Methods inherited from class java.lang.Object

`equals, getClass, hashCode, notify, notifyAll, wait, wait, wait`
• ### Constructor Detail

• #### Normal

```public Normal(double mean,
double standardDeviation,
DoubleRandomEngine randomGenerator)```
Constructs a normal (gauss) distribution. Example: mean=0.0, standardDeviation=1.0.
• ### Method Detail

• #### cdf

`public double cdf(double x)`
Returns the cumulative distribution function.
• #### nextDouble

`public double nextDouble()`
Returns a random number from the distribution.
Specified by:
`nextDouble` in class `AbstractDoubleDistribution`
• #### nextDouble

```public double nextDouble(double mean,
double standardDeviation)```
Returns a random number from the distribution; bypasses the internal state.
• #### pdf

`public double pdf(double x)`
Returns the probability distribution function.
• #### setState

```public void setState(double mean,
double standardDeviation)```
Sets the mean and variance.
• #### staticNextDouble

```public static double staticNextDouble(double mean,
double standardDeviation)```
Returns a random number from the distribution with the given mean and standard deviation.
• #### toString

`public String toString()`
Returns a String representation of the receiver.
Overrides:
`toString` in class `Object`
Parallel Colt 0.10.1