EmpiricalDistribution

java.lang.Object
- smile.stat.distribution.AbstractDistribution
- - smile.stat.distribution.DiscreteDistribution
  - - smile.stat.distribution.EmpiricalDistribution

All Implemented Interfaces:

java.io.Serializable, Distribution
```
public class EmpiricalDistribution
extends DiscreteDistribution
```
An empirical distribution function or empirical cdf, is a cumulative probability distribution function that concentrates probability 1/n at each of the n numbers in a sample. As n grows the empirical distribution will getting closer to the true distribution. Empirical distribution is a very important estimator in Statistics. In particular, the Bootstrap method rely heavily on the empirical distribution.

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

double[] p
The probabilities for each x.

Fields
Modifier and Type	Field and Description
`double[]`	`p` The probabilities for each x.

Constructor Summary

Constructors
Constructor and Description

EmpiricalDistribution(double[] prob)
Constructor.

EmpiricalDistribution(double[] prob, IntSet x)
Constructor.

Constructors
Constructor and Description
`EmpiricalDistribution(double[] prob)` Constructor.
`EmpiricalDistribution(double[] prob, IntSet x)` Constructor.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`cdf(double k)` Cumulative distribution function.
`double`	`entropy()` Shannon entropy of the distribution.
`static EmpiricalDistribution`	`fit(int[] data)` Estimates the distribution.
`static EmpiricalDistribution`	`fit(int[] data, IntSet x)` Estimates the distribution.
`int`	`length()` The number of parameters of the distribution.
`double`	`logp(int k)` The probability mass function in log scale.
`double`	`mean()` The mean of distribution.
`double`	`p(int k)` The probability mass function.
`double`	`quantile(double p)` The quantile, the probability to the left of quantile is p.
`double`	`rand()` Generates a random number following this distribution.
`int[]`	`randi(int n)` Generates a set of integer random numbers following this discrete distribution.
`double`	`sd()` The standard deviation of distribution.
`java.lang.String`	`toString()`
`double`	`variance()` The variance of distribution.

Methods inherited from class smile.stat.distribution.DiscreteDistribution
likelihood, logLikelihood, logp, p, quantile, randi

Methods inherited from class smile.stat.distribution.AbstractDistribution
inverseTransformSampling, quantile, quantile, rejection

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

Methods inherited from interface smile.stat.distribution.Distribution
likelihood, logLikelihood, rand

- Field Detail
  - p
```
public final double[] p
```
    The probabilities for each x.
- Constructor Detail
  - EmpiricalDistribution
```
public EmpiricalDistribution(double[] prob)
```
    Constructor.
    
    Parameters:
    
    prob - the probabilities.
  - EmpiricalDistribution
```
public EmpiricalDistribution(double[] prob,
                             IntSet x)
```
    Constructor.
    
    Parameters:
    
    prob - the probabilities.
    
    x - the values of random variable.
- Method Detail
  - fit
```
public static EmpiricalDistribution fit(int[] data)
```
    Estimates the distribution.
    
    Parameters:
    
    data - the training data.
  - fit
```
public static EmpiricalDistribution fit(int[] data,
                                        IntSet x)
```
    Estimates the distribution. Sometimes, the data may not contain all possible values. In this case, the user should provide the value set.
    
    Parameters:
    
    data - the training data.
    
    x - the value set.
  - length
```
public int length()
```
    Description copied from interface: Distribution
    
    The number of parameters of the distribution. The "length" is in the sense of the minimum description length principle.
  - mean
```
public double mean()
```
    Description copied from interface: Distribution
    
    The mean of distribution.
  - variance
```
public double variance()
```
    Description copied from interface: Distribution
    
    The variance of distribution.
  - sd
```
public double sd()
```
    Description copied from interface: Distribution
    
    The standard deviation of distribution.
  - entropy
```
public double entropy()
```
    Description copied from interface: Distribution
    
    Shannon entropy of the distribution.
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object
  - rand
```
public double rand()
```
    Description copied from interface: Distribution
    
    Generates a random number following this distribution.
  - randi
```
public int[] randi(int n)
```
    Description copied from class: DiscreteDistribution
    
    Generates a set of integer random numbers following this discrete distribution.
    
    Overrides:
    
    randi in class DiscreteDistribution
  - p
```
public double p(int k)
```
    Description copied from class: DiscreteDistribution
    
    The probability mass function.
    
    Specified by:
    
    p in class DiscreteDistribution
  - logp
```
public double logp(int k)
```
    Description copied from class: DiscreteDistribution
    
    The probability mass function in log scale.
    
    Specified by:
    
    logp in class DiscreteDistribution
  - cdf
```
public double cdf(double k)
```
    Description copied from interface: Distribution
    
    Cumulative distribution function. That is the probability to the left of x.
  - quantile
```
public double quantile(double p)
```
    Description copied from interface: Distribution
    
    The quantile, the probability to the left of quantile is p. It is actually the inverse of cdf.

Class EmpiricalDistribution

Field Summary

Constructor Summary

Method Summary

Methods inherited from class smile.stat.distribution.DiscreteDistribution

Methods inherited from class smile.stat.distribution.AbstractDistribution

Methods inherited from class java.lang.Object

Methods inherited from interface smile.stat.distribution.Distribution

Field Detail

p

Constructor Detail

EmpiricalDistribution

EmpiricalDistribution

Method Detail

fit

fit

length

mean

variance

sd

entropy

toString

rand

randi

p

logp

cdf

quantile