ChiSquaredTest Class

Chi-squared goodness-of-fit test.

For a list of all members of this type, see ChiSquaredTest Members.

System.Object
Imsl.Stat.ChiSquaredTest

public class ChiSquaredTest

Thread Safety

Public static (Shared in Visual Basic) members of this type are safe for multithreaded operations. Instance members are not guaranteed to be thread-safe.

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.

Requirements

Namespace: Imsl.Stat

Assembly: ImslCS (in ImslCS.dll)

ChiSquaredTest Class

Thread Safety

Remarks

Requirements

See Also