
SSJ V. 2.6. 

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java.lang.Object umontreal.iro.lecuyer.probdist.DiscreteDistributionInt
public abstract class DiscreteDistributionInt
Classes implementing discrete distributions over the integers should inherit from this class. It specifies the signatures of methods for computing the mass function (or probability) p(x) = P[X = x], distribution function F(x), complementary distribution function bar(F)(x), and inverse distribution function F^{1}(u), for a random variable X with a discrete distribution over the integers.
WARNING: the complementary distribution function is defined as bar(F)(j) = P[X >= j] (for integers j, so that for discrete distributions in SSJ, F(j) + bar(F)(j)≠1 since both include the term P[X = j].
The implementing classes provide both static and nonstatic methods
to compute the above functions.
The nonstatic methods require the creation of an object of
class DiscreteDistributionInt
;
all the nonnegligible terms of the mass and distribution functions will be
precomputed by the constructor and kept in arrays. Subsequent accesses
will be very fast.
The static methods do not require the construction of an object.
These static methods are not specified in this abstract class because
the number and types of their parameters depend on the distribution.
When methods have to be called several times
with the same parameters for the distributions,
it is usually more efficient to create an object and use its nonstatic
methods instead of the static ones.
This trades memory for speed.
Field Summary  

static double 
EPSILON
Environment variable that determines what probability terms can be considered as negligible when building precomputed tables for distribution and mass functions. 
Constructor Summary  

DiscreteDistributionInt()

Method Summary  

double 
barF(double x)
Returns bar(F)(x), the complementary distribution function. 
double 
barF(int x)
Returns bar(F)(x), the complementary distribution function. 
double 
cdf(double x)
Returns the distribution function F evaluated at x (see). 
abstract double 
cdf(int x)
Returns the distribution function F evaluated at x (see). 
int 
getXinf()
Returns the lower limit x_{a} of the support of the probability mass function. 
int 
getXsup()
Returns the upper limit x_{b} of the support of the probability mass function. 
double 
inverseF(double u)
Returns the inverse distribution function F^{1}(u), where 0 <= u <= 1. 
int 
inverseFInt(double u)
Returns the inverse distribution function F^{1}(u), where 0 <= u <= 1. 
abstract double 
prob(int x)
Returns p(x), the probability of x. 
Methods inherited from class java.lang.Object 

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Methods inherited from interface umontreal.iro.lecuyer.probdist.Distribution 

getMean, getParams, getStandardDeviation, getVariance 
Field Detail 

public static double EPSILON
DiscreteDistribution
objects
(such as those of class PoissonDist
, etc.), but are computed
directly each time they are needed (which should be very seldom).
The default value is set to 10^{16}.
Constructor Detail 

public DiscreteDistributionInt()
Method Detail 

public abstract double prob(int x)
x
 value at which the mass function must be evaluated
public double cdf(double x)
cdf
(int) method.
cdf
in interface Distribution
x
 value at which the distribution function must be evaluated
public abstract double cdf(int x)
x
 value at which the distribution function must be evaluated
public double barF(double x)
barF
(int) method.
barF
in interface Distribution
x
 value at which the complementary distribution function
must be evaluated
public double barF(int x)
x
 value at which the complementary distribution function
must be evaluated
public int getXinf()
public int getXsup()
public double inverseF(double u)
inverseF
in interface Distribution
u
 value in the interval (0, 1) for which
the inverse distribution function is evaluated
IllegalArgumentException
 if u is not in the interval (0, 1)
ArithmeticException
 if the inverse cannot be computed,
for example if it would give infinity in a theoritical contextpublic int inverseFInt(double u)
u
 value in the interval (0, 1) for which
the inverse distribution function is evaluated
IllegalArgumentException
 if u is not in the interval (0, 1)
ArithmeticException
 if the inverse cannot be computed,
for example if it would give infinity in a theoritical context

SSJ V. 2.6. 

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