BinomialDistribution (NMDEV 1.2.9 API)

java.lang.Object
- dev.nm.stat.distribution.univariate.BinomialDistribution

All Implemented Interfaces:

ProbabilityDistribution
```
public class BinomialDistribution
extends Object
implements ProbabilityDistribution
```
The binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. For N much larger than n, the binomial distribution is a good approximation of hypergeometric distribution.

See Also:

Wikipedia: Binomial distribution

Constructor Summary

Constructors
Constructor and Description

BinomialDistribution(int n, double p)
Construct a Binomial distribution.

Constructors
Constructor and Description
`BinomialDistribution(int n, double p)` Construct a Binomial distribution.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`cdf(double x)` Gets the cumulative probability F(x) = Pr(X ≤ x).
`double`	`density(double x)` This is the probability mass function.
`double`	`entropy()` Gets the entropy of this distribution.
`double`	`kurtosis()` Gets the excess kurtosis of this distribution.
`double`	`mean()` Gets the mean of this distribution.
`double`	`median()` Gets the median of this distribution.
`double`	`moment(double t)` The moment generating function is the expected value of \(e^{tX}\).
`double`	`quantile(double u)` Gets the quantile, the inverse of the cumulative distribution function.
`double`	`skew()` Gets the skewness of this distribution.
`double`	`variance()` Gets the variance of this distribution.

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

- Constructor Detail
  - BinomialDistribution
```
public BinomialDistribution(int n,
                            double p)
```
    Construct a Binomial distribution.
    
    Parameters:
    
    n - the number of trials, a natural number
    
    p - the success probability in each trial, [0, 1]
- Method Detail
  - mean
```
public double mean()
```
    Description copied from interface: ProbabilityDistribution
    
    Gets the mean of this distribution.
    
    Specified by:
    
    mean in interface ProbabilityDistribution
    
    Returns:
    
    the mean
    
    See Also:
    
    Wikipedia: Expected value
  - median
```
public double median()
```
    Gets the median of this distribution.
    The result is rounded rounded down to an integer.
    
    Specified by:
    
    median in interface ProbabilityDistribution
    
    Returns:
    
    median
    
    See Also:
    
    Wikipedia: Median
  - variance
```
public double variance()
```
    Description copied from interface: ProbabilityDistribution
    
    Gets the variance of this distribution.
    
    Specified by:
    
    variance in interface ProbabilityDistribution
    
    Returns:
    
    the variance
    
    See Also:
    
    Wikipedia: Variance
  - skew
```
public double skew()
```
    Description copied from interface: ProbabilityDistribution
    
    Gets the skewness of this distribution.
    
    Specified by:
    
    skew in interface ProbabilityDistribution
    
    Returns:
    
    the skewness
    
    See Also:
    
    Wikipedia: Skewness
  - kurtosis
```
public double kurtosis()
```
    Description copied from interface: ProbabilityDistribution
    
    Gets the excess kurtosis of this distribution.
    
    Specified by:
    
    kurtosis in interface ProbabilityDistribution
    
    Returns:
    
    the excess kurtosis
    
    See Also:
    
    Wikipedia: Kurtosis
  - cdf
```
public double cdf(double x)
```
    Gets the cumulative probability F(x) = Pr(X ≤ x).
    
    Specified by:
    
    cdf in interface ProbabilityDistribution
    
    Parameters:
    
    x - the number of success trials, an integer; rounded down to the closest integer if x is not an integer
    
    Returns:
    
    cdf(x)
    
    See Also:
    
    Wikipedia: Cumulative distribution function
  - quantile
```
public double quantile(double u)
```
    Gets the quantile, the inverse of the cumulative distribution function. It is the value below which random draws from the distribution would fall u×100 percent of the time. \[ \begin{gathered} F^{-1}(u) = x, such that \\ Pr(X \le x) = u \end{gathered} \] This may not always exist.
    Uses the Cornish-Fisher Expansion to include a skewness correction to a normal approximation. This gives an initial value which never seems to be off by more than 1 or 2. A search is then conducted of values close to this initial start point.
    
    Specified by:
    
    quantile in interface ProbabilityDistribution
    
    Parameters:
    
    u - a quantile
    
    Returns:
    
    qbinom(u)
    
    See Also:
    
    qbinom
  - density
```
public double density(double x)
```
    This is the probability mass function.
    Specified by:
    
    density in interface ProbabilityDistribution
    
    Parameters:
    
    x - the number of success trials, an integer; rounded down to the closest integer if x is not an integer
    
    Returns:
    
    pmf(x)
    
    See Also:
    Wikipedia: Probability density function
    
    Wikipedia: Probability mass function
  - entropy
```
public double entropy()
```
    Description copied from interface: ProbabilityDistribution
    
    Gets the entropy of this distribution.
    
    Specified by:
    
    entropy in interface ProbabilityDistribution
    
    Returns:
    
    the entropy
    
    See Also:
    
    Wikipedia: Entropy (information theory)
  - moment
```
public double moment(double t)
```
    Description copied from interface: ProbabilityDistribution
    
    The moment generating function is the expected value of \(e^{tX}\). That is, \[ E(e^{tX}) \] This may not always exist.
    
    Specified by:
    
    moment in interface ProbabilityDistribution
    
    Parameters:
    
    t - t
    
    Returns:
    
    E(exp(tX))
    
    See Also:
    
    Wikipedia: Moment-generating function

Class BinomialDistribution

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

BinomialDistribution

Method Detail

mean

median

variance

skew

kurtosis

cdf

quantile

density

entropy

moment