org.hipparchus.distribution

## Interface IntegerDistribution

• ### Method Summary

All Methods
Modifier and Type Method and Description
double cumulativeProbability(int x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X <= 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.
int getSupportLowerBound()
Access the lower bound of the support.
int getSupportUpperBound()
Access the upper bound of the support.
int 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.
double logProbability(int x)
For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm.
double probability(int x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
double probability(int x0, int x1)
For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
• ### Method Detail

• #### logProbability

double logProbability(int x)
For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm. In other words, this method represents the logarithm of the probability mass function (PMF) for the distribution. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of probability(int).
Parameters:
x - the point at which the PMF is evaluated
Returns:
the logarithm of the value of the probability mass function at x
• #### probability

double probability(int 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 x
• #### probability

double probability(int x0,
int x1)
throws MathIllegalArgumentException
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 will take a value between x0 and x1, excluding the lower and including the upper endpoint
Throws:
MathIllegalArgumentException - if x0 > x1
• #### cumulativeProbability

double cumulativeProbability(int 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
• #### inverseCumulativeProbability

int inverseCumulativeProbability(double p)
throws MathIllegalArgumentException
Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is
• inf{x in Z | P(X<=x) >= p} for 0 < p <= 1,
• inf{x in Z | P(X<=x) > 0} for p = 0.
If the result exceeds the range of the data type int, then Integer.MIN_VALUE or Integer.MAX_VALUE is returned.
Parameters:
p - the cumulative probability
Returns:
the smallest p-quantile of this distribution (largest 0-quantile for p = 0)
Throws:
MathIllegalArgumentException - 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 or Double.NaN if it is not defined)
• #### getSupportLowerBound

int 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 Z | P(X <= x) > 0}.

Returns:
lower bound of the support (Integer.MIN_VALUE for negative infinity)
• #### getSupportUpperBound

int 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 (Integer.MAX_VALUE for positive infinity)
• #### isSupportConnected

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