Namespace:
Imsl.Stat
Assembly:
ImslCS (in ImslCS.dll) Version: 6.5.0.0
Syntax
| C# |
|---|
[SerializableAttribute] public class ChiSquaredTest |
| Visual Basic (Declaration) |
|---|
<SerializableAttribute> _ Public Class ChiSquaredTest |
| Visual C++ |
|---|
[SerializableAttribute] public ref class ChiSquaredTest |
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 
and
, 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
, where m is the
number of categories and 
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.
