Package org.hipparchus.distribution
Interface IntegerDistribution

 All Known Implementing Classes:
AbstractIntegerDistribution
,BinomialDistribution
,EnumeratedIntegerDistribution
,GeometricDistribution
,HypergeometricDistribution
,PascalDistribution
,PoissonDistribution
,UniformIntegerDistribution
,ZipfDistribution
public interface IntegerDistribution
Interface for discrete distributions.


Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method Description double
cumulativeProbability(int x)
For a random variableX
whose values are distributed according to this distribution, this method returnsP(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. whether all integers between the lower and upper bound of the support are included in the support.double
logProbability(int x)
For a random variableX
whose values are distributed according to this distribution, this method returnslog(P(X = x))
, wherelog
is the natural logarithm.double
probability(int x)
For a random variableX
whose values are distributed according to this distribution, this method returnsP(X = x)
.double
probability(int x0, int x1)
For a random variableX
whose values are distributed according to this distribution, this method returnsP(x0 < X <= x1)
.



Method Detail

logProbability
double logProbability(int x)
For a random variableX
whose values are distributed according to this distribution, this method returnslog(P(X = x))
, wherelog
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 ofprobability(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 variableX
whose values are distributed according to this distribution, this method returnsP(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 variableX
whose values are distributed according to this distribution, this method returnsP(x0 < X <= x1)
. Parameters:
x0
 the exclusive lower boundx1
 the inclusive upper bound Returns:
 the probability that a random variable with this distribution
will take a value between
x0
andx1
, excluding the lower and including the upper endpoint  Throws:
MathIllegalArgumentException
 ifx0 > x1

cumulativeProbability
double cumulativeProbability(int x)
For a random variableX
whose values are distributed according to this distribution, this method returnsP(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 variableX
distributed according to this distribution, the returned value isinf{x in Z  P(X<=x) >= p}
for0 < p <= 1
,inf{x in Z  P(X<=x) > 0}
forp = 0
.
int
, thenInteger.MIN_VALUE
orInteger.MAX_VALUE
is returned. Parameters:
p
 the cumulative probability Returns:
 the smallest
p
quantile of this distribution (largest 0quantile forp = 0
)  Throws:
MathIllegalArgumentException
 ifp < 0
orp > 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
orDouble.NaN
if it is not defined)

getSupportLowerBound
int getSupportLowerBound()
Access the lower bound of the support. This method must return the same value asinverseCumulativeProbability(0)
. In other words, this method must returninf {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 asinverseCumulativeProbability(1)
. In other words, this method must returninf {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

