NormalDistribution (JMSL Numerical Library)

java.lang.Object
- com.imsl.stat.NormalDistribution

All Implemented Interfaces:

Distribution, ProbabilityDistribution, Serializable
```
public class NormalDistribution
extends Object
implements ProbabilityDistribution, Serializable
```
Evaluates the normal (Gaussian) probability density for a given set of data.
NormalDistribution evaluates the normal probability density of a given set of data, xData. If parameters are not supplied, the eval method fits the normal probability density function to the data by first calculating the mean and standard deviation of xData. The normal probability density function is defined as:
$f(x) = frac{1}{sigma sqrt{2pi}} e^{frac{{-(x - mu)}^2}{{2 sigma}^2}}$
where and are the mean and standard deviation.

The DataMining package class NaiveBayesClassifier uses NormalDistribution as the default method to train continuous data.

See Also:
Example, Serialized Form

Constructor Summary

Constructors
Constructor and Description

NormalDistribution()

Constructors
Constructor and Description
`NormalDistribution()`

Method Summary

Methods
Modifier and Type	Method and Description
`double[]`	`eval(double[] xData)` Fits a normal (Gaussian) probability distribution to `xData` and returns the probability density at each value.
`double[]`	`eval(double[] xData, Object[] parameters)` Evaluates a normal (Gaussian) probability distribution with the given parameters at each point in `xData` and returns the probability density at each value.
`double`	`eval(double xData, Object[] parameters)` Evaluates a normal (Gaussian) probability density at a given point `xData`.
`double`	`getMean()` Returns the population mean of `xData`.
`Object[]`	`getParameters()` Returns the current parameters of the normal probability density function.
`double`	`getStandardDeviation()` Returns the population standard deviation.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - NormalDistribution
```
public NormalDistribution()
```
- Method Detail
  - eval
```
public double[] eval(double[] xData)
```
    Fits a normal (Gaussian) probability distribution to xData and returns the probability density at each value.
    
    Specified by:
    
    eval in interface Distribution
    
    Parameters:
    xData - a double array representing the points at which the normal probability distribution function is to be evaluated
    
    Returns:
    a double array representing the normal probability density at each value in xData
  - eval
```
public double[] eval(double[] xData,
            Object[] parameters)
```
    Evaluates a normal (Gaussian) probability distribution with the given parameters at each point in xData and returns the probability density at each value.
    
    Specified by:
    
    eval in interface ProbabilityDistribution
    
    Parameters:
    xData - a double array representing the points at which the normal probability distribution function is to be evaluated
    parameters - an Object array representing the parameters used to evaluate the normal probability density function, see method getParameters
    
    Returns:
    a double array representing the normal probability density of each value in xData
  - eval
```
public double eval(double xData,
          Object[] parameters)
```
    Evaluates a normal (Gaussian) probability density at a given point xData.
    
    Specified by:
    
    eval in interface ProbabilityDistribution
    
    Parameters:
    xData - a double containing the point at which the normal probability density function is to be evaluated
    parameters - an Object array representing the parameters used to evaluate the normal probability density, see method getParameters
    
    Returns:
    a double representing the normal probability density at xData
  - getMean
```
public double getMean()
```
    Returns the population mean of xData.
    
    Returns:
    a double representing the population mean of xData
  - getParameters
```
public Object[] getParameters()
```
    Returns the current parameters of the normal probability density function.
    
    Specified by:
    
    getParameters in interface ProbabilityDistribution
    
    Returns:
    an Object array containing the parameters resulting from the last invocation of the (Distribution) eval method with the following signature, double[] eval(double[] xData). This Object array can be used as input to the eval methods that require an Object array of distribution parameters as input.
  - getStandardDeviation
```
public double getStandardDeviation()
```
    Returns the population standard deviation.
    
    Returns:
    a double representing the population standard devation of xData

Class NormalDistribution

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

NormalDistribution

Method Detail

eval

eval

eval

getMean

getParameters

getStandardDeviation