Package org.drip.measure.gamma

Class R1InvariantScaleParameterEstimator

java.lang.Object

org.drip.measure.gamma.R1InvariantScaleParameterEstimator

public class R1InvariantScaleParameterEstimator
extends java.lang.Object

R1InvariantScaleParameterEstimator implements the Scale Parameter Estimator using Scale-Invariant Prior for the Scale Parameter under a Sequence of Observations. The References are:

• Devroye, L. (1986): Non-Uniform Random Variate Generation Springer-Verlag New York
• Gamma Distribution (2019): Gamma Distribution https://en.wikipedia.org/wiki/Chi-squared_distribution
• Louzada, F., P. L. Ramos, and E. Ramos (2019): A Note on Bias of Closed-Form Estimators for the Gamma Distribution Derived From Likelihood Equations The American Statistician 73 (2) 195-199
• Minka, T. (2002): Estimating a Gamma distribution https://tminka.github.io/papers/minka-gamma.pdf
• Ye, Z. S., and N. Chen (2017): Closed-Form Estimators for the Gamma Distribution Derived from Likelihood Equations The American Statistician 71 (2) 177-181

It provides the following Functionality:

• Construct an Instance of R1InvariantScaleParameterEstimator from the Array of Realizations
• R1InvariantScaleParameterEstimator Constructor
• Retrieve the Samples used for the ML Estimate
• Infer the Scale Parameter Distribution
• Infer the Distribution Moment's Scale Parameter

Module	Computational Core Module
Library	Numerical Analysis Library
Project	Rd Continuous/Discrete Probability Measures
Package	R1 Gamma Distribution Implementation/Properties

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
R1InvariantScaleParameterEstimator(R1Sample sample)	R1InvariantScaleParameterEstimator Constructor

Method Summary

Modifier and Type	Method	Description
static R1InvariantScaleParameterEstimator	FromRealizationArray(double[] realizationArray)	Construct an Instance of R1InvariantScaleParameterEstimator from the Array of Realizations
R1UnivariateNormal	inferScaleParameterDistribution(double shape)	Infer the Scale Parameter Distribution
double	inferScaleParameterDistributionMoment(double shape, int moment, R1ToR1 gammaEstimator)	Infer the Distribution Moment's Scale Parameter
R1Sample	sample()	Retrieve the Samples used for the ML Estimate

Methods inherited from class java.lang.Object

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

Constructor Details

R1InvariantScaleParameterEstimator

public R1InvariantScaleParameterEstimator(R1Sample sample)
                                   throws java.lang.Exception

R1InvariantScaleParameterEstimator Constructor

Parameters:

sample - The Sample

Throws:

java.lang.Exception - Thrown of the Inputs are Invalid

Method Details

FromRealizationArray

public static final R1InvariantScaleParameterEstimator FromRealizationArray(double[] realizationArray)

Construct an Instance of R1InvariantScaleParameterEstimator from the Array of Realizations

Parameters:

realizationArray - The Realization Array

Returns:

Instance of R1InvariantScaleParameterEstimator

sample

public R1Sample sample()

Retrieve the Samples used for the ML Estimate

Returns:

Samples used for the ML Estimate

inferScaleParameterDistribution

public R1UnivariateNormal inferScaleParameterDistribution(double shape)

Infer the Scale Parameter Distribution

Parameters:

shape - Shape Parameter

Returns:

The Scale Parameter Distribution

inferScaleParameterDistributionMoment

public double inferScaleParameterDistributionMoment(double shape,
int moment,
R1ToR1 gammaEstimator)
                                             throws java.lang.Exception

Infer the Distribution Moment's Scale Parameter

Parameters:

shape - Shape Parameter

moment - Moment Parameter

gammaEstimator - Gamma Estimator

Returns:

The Scale Parameter

Throws:

java.lang.Exception - Thrown if the Scale Parameter cannot be estimated