org.apache.commons.statistics.distribution

## Interface ContinuousDistribution

• ### Nested Class Summary

Nested Classes
Modifier and Type Interface and Description
static interface  ContinuousDistribution.Sampler
Distribution sampling functionality.
• ### Method Summary

All Methods
Modifier and Type Method and Description
ContinuousDistribution.Sampler createSampler(UniformRandomProvider rng)
Creates a sampler.
double cumulativeProbability(double x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
double density(double x)
Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
double getMean()
Gets the mean of this distribution.
double getSupportLowerBound()
Gets the lower bound of the support.
double getSupportUpperBound()
Gets the upper bound of the support.
double getVariance()
Gets the variance of this distribution.
double inverseCumulativeProbability(double p)
Computes the quantile function of this distribution.
default double inverseSurvivalProbability(double p)
Computes the inverse survival probability function of this distribution.
default double logDensity(double x)
Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
default double probability(double x0, double x1)
For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
default double survivalProbability(double x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X > x).
• ### Method Detail

• #### 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 - Point at which the PDF is evaluated.
Returns:
the value of the probability density function at x.
• #### probability

default double probability(double x0,
double x1)
For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1). The default implementation uses the identity P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)
Parameters:
x0 - Lower bound (exclusive).
x1 - Upper bound (inclusive).
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:
IllegalArgumentException - if x0 > x1.
• #### logDensity

default double logDensity(double x)
Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
Parameters:
x - Point at which the PDF is evaluated.
Returns:
the logarithm of the value of the probability density function at 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 - 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.
• #### survivalProbability

default double survivalProbability(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 complementary cumulative distribution function.

By default, this is defined as 1 - cumulativeProbability(x), but the specific implementation may be more accurate.

Parameters:
x - Point at which the survival function is evaluated.
Returns:
the probability that a random variable with this distribution takes a value greater than x.
• #### inverseCumulativeProbability

double inverseCumulativeProbability(double p)
Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is:

$x = \begin{cases} \inf \{ x \in \mathbb R : P(X \le x) \ge p\} & \text{for } 0 \lt p \le 1 \\ \inf \{ x \in \mathbb R : P(X \le x) \gt 0 \} & \text{for } p = 0 \end{cases}$

Parameters:
p - Cumulative probability.
Returns:
the smallest p-quantile of this distribution (largest 0-quantile for p = 0).
Throws:
IllegalArgumentException - if p < 0 or p > 1.
• #### inverseSurvivalProbability

default double inverseSurvivalProbability(double p)
Computes the inverse survival probability function of this distribution. For a random variable X distributed according to this distribution, the returned value is:

$x = \begin{cases} \inf \{ x \in \mathbb R : P(X \ge x) \le p\} & \text{for } 0 \le p \lt 1 \\ \inf \{ x \in \mathbb R : P(X \ge x) \lt 1 \} & \text{for } p = 1 \end{cases}$

By default, this is defined as inverseCumulativeProbability(1 - p), but the specific implementation may be more accurate.

Parameters:
p - Survival probability.
Returns:
the smallest (1-p)-quantile of this distribution (largest 0-quantile for p = 1).
Throws:
IllegalArgumentException - if p < 0 or p > 1.
• #### getMean

double getMean()
Gets the mean of this distribution.
Returns:
the mean.
• #### getVariance

double getVariance()
Gets the variance of this distribution.
Returns:
the variance.
• #### getSupportLowerBound

double getSupportLowerBound()
Gets the lower bound of the support. It must return the same value as inverseCumulativeProbability(0), i.e. $$\inf \{ x \in \mathbb R : P(X \le x) \gt 0 \}$$.
Returns:
the lower bound of the support.
• #### getSupportUpperBound

double getSupportUpperBound()
Gets the upper bound of the support. It must return the same value as inverseCumulativeProbability(1), i.e. $$\inf \{ x \in \mathbb R : P(X \le x) = 1 \}$$.
Returns:
the upper bound of the support.
• #### createSampler

ContinuousDistribution.Sampler createSampler(UniformRandomProvider rng)
Creates a sampler.
Parameters:
rng - Generator of uniformly distributed numbers.
Returns:
a sampler that produces random numbers according this distribution.