Mises

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riso.distributions
Class Mises

java.lang.Object
  riso.distributions.AbstractDistribution
      riso.distributions.Mises

All Implemented Interfaces:: ConditionalDistribution, Distribution, java.io.Serializable

public class Mises
extends AbstractDistribution

An instance of this class represent a von Mises distribution, also called a circular Gaussian distribution.

Field Summary

double a
          The location parameter of this distribution.

double b
          The scale parameter of this distribution.

Fields inherited from class riso.distributions.AbstractDistribution

associated_variable

Constructor Summary

Mises()
          Construct an instance with default parameters, namely a==0 and b==1.

Mises(double a, double b)
          Constructs a lognormal with the specified parameters.

Method Summary

double[] effective_support(double epsilon)
          Returns an interval which contains almost all of the mass of this distribution.

double expected_value()
          Returns the expected value of this distribution.

java.lang.String format_string(java.lang.String leading_ws)
          Formats a string representation of this distribution.

static double I10_ratio(double u)
          Computes the ratio I1(u)/I0(u) for the argument u.

double log_prior()
          Computes the log of the prior probability of the parameters of this distribution, assuming some prior distribution has been established.

int ndimensions()
          Returns the number of dimensions in which this distribution lives.

double p(double[] x)
          Compute the density at the point x.

void pretty_input(riso.general.SmarterTokenizer st)
          Read an instance of this distribution from an input stream.

double[] random()
          Returns an instance of a random variable from this distribution.

double sqrt_variance()
          Returns the square root of the variance of this distribution.

double update(double[][] theta, double[] responsibility, int niter_max, double stopping_criterion)
          Uses data to modify the parameters of the distribution.

double weighted_nll(double[][] theta, double[] responsibility)
          Computes the negative log likelihood, weighting each case by the responsibility.

Methods inherited from class riso.distributions.AbstractDistribution

cdf, clone, get_density, get_nstates, initial_mix, log_p, ndimensions_child, ndimensions_parent, p, parse_string, pretty_output, random, set_variable, toString

Methods inherited from class java.lang.Object

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

Field Detail

a

public double a

The location parameter of this distribution. Don't modify this parameter -- create a new instance if a different parameter is needed.

b

public double b

The scale parameter of this distribution. Don't modify this parameter -- create a new instance if a different parameter is needed.

Constructor Detail

Mises

public Mises()

Construct an instance with default parameters, namely a==0 and b==1.

Mises

public Mises(double a,
             double b)

Constructs a lognormal with the specified parameters.

Method Detail

ndimensions

public int ndimensions()

Returns the number of dimensions in which this distribution lives. This number is always 1.

Specified by:: ndimensions in interface Distribution
Overrides:: ndimensions in class AbstractDistribution

p

public double p(double[] x)

Compute the density at the point x. Density function given by Weisstein, ``Von Mises Distribution.''

log_prior

public double log_prior()
                 throws java.lang.Exception

Computes the log of the prior probability of the parameters of this distribution, assuming some prior distribution has been established. This may not be meaningful.

Specified by:: log_prior in interface Distribution
Overrides:: log_prior in class AbstractDistribution

random

public double[] random()
                throws java.lang.Exception

Returns an instance of a random variable from this distribution.

Specified by:: random in interface Distribution
Overrides:: random in class AbstractDistribution

update

public double update(double[][] theta,
                     double[] responsibility,
                     int niter_max,
                     double stopping_criterion)
              throws java.lang.Exception

Uses data to modify the parameters of the distribution. This method implements the maximum likelihood formulas worked out in hand-written notes, 8 Dec 2001. Let theta[i] be a list of angles. Let S = \sum_i sin theta[i]. Let C = \sum_i cos theta[i]. Let R^2 = S^2 + C^2. Then the maximum likelihood estimate of the parameter a is atan2(S,C), and the m.l. estimate of b is a solution of (sin \hat a)/S R^2/n = I1(b)/I0(b), where n is the number of data and I0, I1 are the modified Bessel functions of the first kind and orders zero and one, respectively.

Specified by:: update in interface Distribution
Overrides:: update in class AbstractDistribution

I10_ratio

public static double I10_ratio(double u)

Computes the ratio I1(u)/I0(u) for the argument u.

weighted_nll

public double weighted_nll(double[][] theta,
                           double[] responsibility)

Computes the negative log likelihood, weighting each case by the responsibility.

expected_value

public double expected_value()

Returns the expected value of this distribution.

Specified by:: expected_value in interface Distribution
Overrides:: expected_value in class AbstractDistribution

sqrt_variance

public double sqrt_variance()
                     throws java.lang.Exception

Returns the square root of the variance of this distribution.

Specified by:: sqrt_variance in interface Distribution
Overrides:: sqrt_variance in class AbstractDistribution

effective_support

public double[] effective_support(double epsilon)
                           throws java.lang.Exception

Returns an interval which contains almost all of the mass of this distribution. ALWAYS RETURNS [0,2 PI] !!! WE CAN DO BETTER !!!

Specified by:: effective_support in interface Distribution
Overrides:: effective_support in class AbstractDistribution

format_string

public java.lang.String format_string(java.lang.String leading_ws)

Formats a string representation of this distribution. Since the representation is only one line of output, the argument leading_ws is ignored.

Specified by:: format_string in interface ConditionalDistribution
Overrides:: format_string in class AbstractDistribution

pretty_input

public void pretty_input(riso.general.SmarterTokenizer st)
                  throws java.io.IOException

Read an instance of this distribution from an input stream. This is intended for input from a human-readable source; this is different from object serialization.

Overrides:: pretty_input in class AbstractDistribution

Overview

Package

Class

Use

Deprecated

Index

Home >> All >> riso >> [ distributions overview ]

PREV CLASS NEXT CLASS

SUMMARY:

JAVADOC |

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DETAIL: FIELD | CONSTR | METHOD

Field Summary
`double`	`a` The location parameter of this distribution.
`double`	`b` The scale parameter of this distribution.

Constructor Summary
`Mises()` Construct an instance with default parameters, namely `a==0` and `b==1`.
`Mises(double a, double b)` Constructs a lognormal with the specified parameters.

Method Summary
`double[]`	`effective_support(double epsilon)` Returns an interval which contains almost all of the mass of this distribution.
`double`	`expected_value()` Returns the expected value of this distribution.
`java.lang.String`	`format_string(java.lang.String leading_ws)` Formats a string representation of this distribution.
`static double`	`I10_ratio(double u)` Computes the ratio `I1(u)/I0(u)` for the argument `u`.
`double`	`log_prior()` Computes the log of the prior probability of the parameters of this distribution, assuming some prior distribution has been established.
`int`	`ndimensions()` Returns the number of dimensions in which this distribution lives.
`double`	`p(double[] x)` Compute the density at the point `x`.
`void`	`pretty_input(riso.general.SmarterTokenizer st)` Read an instance of this distribution from an input stream.
`double[]`	`random()` Returns an instance of a random variable from this distribution.
`double`	`sqrt_variance()` Returns the square root of the variance of this distribution.
`double`	`update(double[][] theta, double[] responsibility, int niter_max, double stopping_criterion)` Uses data to modify the parameters of the distribution.
`double`	`weighted_nll(double[][] theta, double[] responsibility)` Computes the negative log likelihood, weighting each case by the responsibility.

riso.distributions Class Mises

a

b

Mises

Mises

ndimensions

p

log_prior

random

update

I10_ratio

weighted_nll

expected_value

sqrt_variance

effective_support

format_string

pretty_input

riso.distributions
Class Mises