org.apache.commons.math3.distribution

## Interface RealDistribution

• ### Method Summary

Methods
Modifier and Type Method and Description
`double` `cumulativeProbability(double x)`
For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X <= x)`.
`double` ```cumulativeProbability(double x0, double x1)```
For a random variable `X` whose values are distributed according to this distribution, this method returns `P(x0 < X <= x1)`.
`double` `density(double x)`
Returns the probability density function (PDF) of this distribution evaluated at the specified point `x`.
`double` `getNumericalMean()`
Use this method to get the numerical value of the mean of this distribution.
`double` `getNumericalVariance()`
Use this method to get the numerical value of the variance of this distribution.
`double` `getSupportLowerBound()`
Access the lower bound of the support.
`double` `getSupportUpperBound()`
Access the upper bound of the support.
`double` `inverseCumulativeProbability(double p)`
Computes the quantile function of this distribution.
`boolean` `isSupportConnected()`
Use this method to get information about whether the support is connected, i.e.
`boolean` `isSupportLowerBoundInclusive()`
Use this method to get information about whether the lower bound of the support is inclusive or not.
`boolean` `isSupportUpperBoundInclusive()`
Use this method to get information about whether the upper bound of the support is inclusive or not.
`double` `probability(double x)`
For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X = x)`.
`void` `reseedRandomGenerator(long seed)`
Reseed the random generator used to generate samples.
`double` `sample()`
Generate a random value sampled from this distribution.
`double[]` `sample(int sampleSize)`
Generate a random sample from the distribution.
• ### Method Detail

• #### probability

`double probability(double x)`
For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X = x)`. In other words, this method represents the probability mass function (PMF) for the distribution.
Parameters:
`x` - the point at which the PMF is evaluated
Returns:
the value of the probability mass function at point `x`
• #### density

`double density(double x)`
Returns the probability density function (PDF) of this distribution evaluated at the specified point `x`. In general, the PDF is the derivative of the `CDF`. If the derivative does not exist at `x`, then an appropriate replacement should be returned, e.g. `Double.POSITIVE_INFINITY`, `Double.NaN`, or the limit inferior or limit superior of the difference quotient.
Parameters:
`x` - the point at which the PDF is evaluated
Returns:
the value of the probability density function at point `x`
• #### cumulativeProbability

`double cumulativeProbability(double x)`
For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X <= x)`. In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.
Parameters:
`x` - the point at which the CDF is evaluated
Returns:
the probability that a random variable with this distribution takes a value less than or equal to `x`
• #### cumulativeProbability

```double cumulativeProbability(double x0,
double x1)
throws NumberIsTooLargeException```
For a random variable `X` whose values are distributed according to this distribution, this method returns `P(x0 < X <= x1)`.
Parameters:
`x0` - the exclusive lower bound
`x1` - the inclusive upper bound
Returns:
the probability that a random variable with this distribution takes a value between `x0` and `x1`, excluding the lower and including the upper endpoint
Throws:
`NumberIsTooLargeException` - if `x0 > x1`
• #### inverseCumulativeProbability

```double inverseCumulativeProbability(double p)
throws OutOfRangeException```
Computes the quantile function of this distribution. For a random variable `X` distributed according to this distribution, the returned value is
• `inf{x in R | P(X<=x) >= p}` for `0 < p <= 1`,
• `inf{x in R | P(X<=x) > 0}` for `p = 0`.
Parameters:
`p` - the cumulative probability
Returns:
the smallest `p`-quantile of this distribution (largest 0-quantile for `p = 0`)
Throws:
`OutOfRangeException` - if `p < 0` or `p > 1`
• #### getNumericalMean

`double getNumericalMean()`
Use this method to get the numerical value of the mean of this distribution.
Returns:
the mean or `Double.NaN` if it is not defined
• #### getNumericalVariance

`double getNumericalVariance()`
Use this method to get the numerical value of the variance of this distribution.
Returns:
the variance (possibly `Double.POSITIVE_INFINITY` as for certain cases in `TDistribution`) or `Double.NaN` if it is not defined
• #### getSupportLowerBound

`double getSupportLowerBound()`
Access the lower bound of the support. This method must return the same value as `inverseCumulativeProbability(0)`. In other words, this method must return

`inf {x in R | P(X <= x) > 0}`.

Returns:
lower bound of the support (might be `Double.NEGATIVE_INFINITY`)
• #### getSupportUpperBound

`double getSupportUpperBound()`
Access the upper bound of the support. This method must return the same value as `inverseCumulativeProbability(1)`. In other words, this method must return

`inf {x in R | P(X <= x) = 1}`.

Returns:
upper bound of the support (might be `Double.POSITIVE_INFINITY`)
• #### isSupportLowerBoundInclusive

`boolean isSupportLowerBoundInclusive()`
Use this method to get information about whether the lower bound of the support is inclusive or not.
Returns:
whether the lower bound of the support is inclusive or not
• #### isSupportUpperBoundInclusive

`boolean isSupportUpperBoundInclusive()`
Use this method to get information about whether the upper bound of the support is inclusive or not.
Returns:
whether the upper bound of the support is inclusive or not
• #### isSupportConnected

`boolean isSupportConnected()`
Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support.
Returns:
whether the support is connected or not
• #### reseedRandomGenerator

`void reseedRandomGenerator(long seed)`
Reseed the random generator used to generate samples.
Parameters:
`seed` - the new seed
• #### sample

`double sample()`
Generate a random value sampled from this distribution.
Returns:
a random value.
• #### sample

`double[] sample(int sampleSize)`
Generate a random sample from the distribution.
Parameters:
`sampleSize` - the number of random values to generate
Returns:
an array representing the random sample
Throws:
`NotStrictlyPositiveException` - if `sampleSize` is not positive