ChiSquaredTest Class

Chi-squared goodness-of-fit test.

Inheritance Hierarchy

SystemObject
Imsl.StatChiSquaredTest

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

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[SerializableAttribute]
public class ChiSquaredTest

<SerializableAttribute>
Public Class ChiSquaredTest

[SerializableAttribute]
public ref class ChiSquaredTest

[<SerializableAttribute>]
type ChiSquaredTest =  class end

The ChiSquaredTest type exposes the following members.

Constructors

	Name	Description
	ChiSquaredTest(ICdfFunction, Double, Int32)	Constructor for the Chi-squared goodness-of-fit test.
	ChiSquaredTest(ICdfFunction, Int32, Int32)	Constructor for the Chi-squared goodness-of-fit test

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Methods

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetCellCounts	Returns the cell counts.
	GetCutpoints	Returns the cutpoints.
	GetExpectedCounts	Returns the expected counts.
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	SetCutpoints	Sets the cutpoints.
	SetRange	Sets endpoints of the range of the distribution.
	ToString	Returns a string that represents the current object. (Inherited from Object.)
	Update(Double, Double)	Adds a new observation to the test.
	Update(Double, Double)	Adds new observations to the test.

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Properties

	Name	Description
	ChiSquared	The chi-squared statistic.
	DegreesOfFreedom	Returns the degrees of freedom in chi-squared.
	P	The p-value for the chi-squared statistic.

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Remarks

ChiSquaredTest performs a chi-squared goodness-of-fit test that a random sample of observations is distributed according to a specified theoretical cumulative distribution. The theoretical distribution, which may be continuous, discrete, or a mixture of discrete and continuous distributions, is specified via a user-defined function F where F implements ICdfFunction. Because the user is allowed to specify a range for the observations in the SetRange method, a test that is conditional upon the specified range is performed.

ChiSquaredTest can be constructed in two different ways. The intervals can be specified via the array cutpoints. Otherwise, the number of cutpoints can be given and equiprobable intervals computed by the constructor. The observations are divided into these intervals. Regardless of the method used to obtain them, the intervals are such that the lower endpoint is not included in the interval while the upper endpoint is always included. The user should determine the cutpoints when the cumulative distribution function has discrete elements since ChiSquaredTest cannot determine them in this case.

By default, the lower and upper endpoints of the first and last intervals are $-\infty$ and $+\infty$ , respectively. The method SetRange can be used to change the range.

A tally of counts is maintained for the observations in x as follows:

If the cutpoints are specified by the user, the tally is made in the interval to which belongs, using the user-specified endpoints.

If the cutpoints are determined by the class then the cumulative probability at , , is computed using Cdf.

The tally for is made in interval number $\lfloor mF(x) + 1 \rfloor$ , where m is the number of categories and $\lfloor.\rfloor$ is the function that takes the greatest integer that is no larger than the argument of the function. If the cutpoints are specified by the user, the tally is made in the interval to which belongs using the endpoints specified by the user. Thus, if the computer time required to calculate the cumulative distribution function is large, user-specified cutpoints may be preferred in order to reduce the total computing time.

If the expected count in any cell is less than 1, then a rule of thumb is that the chi-squared approximation may be suspect. A warning message to this effect is issued in this case, as well as when an expected value is less than 5.

Reference

Imsl.Stat Namespace

Other Resources

Example