com.imsl.stat.distributions

Class GammaPD

java.lang.Object

com.imsl.stat.distributions.ProbabilityDistribution

com.imsl.stat.distributions.GammaPD

All Implemented Interfaces:

Serializable, Cloneable

public class GammaPD
extends ProbabilityDistribution
implements Serializable, Cloneable

The gamma probability distribution.

See Also:

Example, Serialized Form

Constructor Summary

Constructors

Constructor and Description
GammaPD() Constructor for the gamma probability distribution.

Method Summary

Modifier and Type	Method and Description
double[]	getParameterLowerBounds() Returns the lower bounds of the parameters.
double[]	getParameterUpperBounds() Returns the upper bounds of the parameters.
double	pdf(double x, double... params) Returns the value of the gamma probability density function.

Methods inherited from class com.imsl.stat.distributions.ProbabilityDistribution

getNumberOfParameters, getPDFGradientApproximation, getPDFHessianApproximation, getRangeOfX, setRangeOfX

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

GammaPD

public GammaPD()

Constructor for the gamma probability distribution.

Method Detail

pdf

public double pdf(double x,
                  double... params)

Returns the value of the gamma probability density function.

The probability density function of the gamma distribution is

$$ f(x; a, b) = x^{a - 1} \frac{1}{{b^{a} \Gamma (a)}} e^{ - {x}/{b}} $$

where \( a > 0\) and \( b> 0\) are the shape and scale parameters, respectively.

Specified by:

pdf in class ProbabilityDistribution

Parameters:

x - a double, the value (quantile) at which to evaluate the pdf

params - a double array specifying the parameters, a and b. The parameters can also be given in the form pdf(x,a,b), where a and b are scalars.

Returns:

a double, the probability density at x given the parameter values

getParameterLowerBounds

public double[] getParameterLowerBounds()

Returns the lower bounds of the parameters.

Specified by:

getParameterLowerBounds in class ProbabilityDistribution

Returns:

a double array containing the lower bounds for \( a > 0\) and \( b> 0\)

getParameterUpperBounds

public double[] getParameterUpperBounds()

Returns the upper bounds of the parameters.

Specified by:

getParameterUpperBounds in class ProbabilityDistribution

Returns:

a double array containing the upper bounds for \( a > 0\) and \( b> 0\)