The ChiSquareSuitableModelTest function performs the chisquare suitable model test upon an observed data sample against a known random variable or probability distribution.  The test attempts to determine if the given sample can be considered to have been drawn from the given random variable or probability distribution by constructing probability categories and applying a goodness-of-fit test

The first parameter X is a one-dimensional rtable of observed data to use in the analysis.

The second parameter F is a random variable or probability distribution that is compared to the observed data set.

The test_options argument can contain one or more of the options shown below.

bins='deduce' or posint

This option indicates the number of bins to use when categorizing data from X and probabilities from F.  If set to 'deduce' (default), the function attempts to determine a reasonable value for this option. This parameter is ignored if the distribution is discrete.

range='deduce' or range

This option indicates the range to use when considering data values - data outside of the range is discarded during processing.  If set to 'deduce' (default), the function attempts to determine a suitable range.

level=float

This option is used to specify the level of the analysis (minimum criteria for the observed data to be considered well-fit to the expected data).  By default, this value is 0.05.

output='report', 'statistic', 'pvalue', 'criticalvalue', 'distribution', 'hypothesis', or list('statistic', 'pvalue', 'criticalvalue', 'distribution', 'hypothesis')

This option is used to specify the desired format of the output from the function.  If 'report' is specified then a module containing all output from this test is returned.  If a single parameter name is specified other than 'report' then that quantity alone is returned.  If a list of parameter names is specified then a list containing those quantities in the specified order will be returned.

This test generates a complete report of all calculations in the form of a userinfo message.  In order to access this report, specify infolevel[Statistics] := 1.

Chi-Square Test for Suitable Probability Model
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Null Hypothesis:
Sample was drawn from specified probability distribution
Alt. Hypothesis:
Sample was not drawn from specified probability distribution

Bins:                    10
Distribution:            ChiSquare(9)
Computed statistic:      4.4
Computed pvalue:         0.883171
Critical value:          16.9189774487099

Result: [Accepted]
There is no statistical evidence against the null hypothesis

Chi-Square Test for Suitable Probability Model
----------------------------------------------
Null Hypothesis:
Sample was drawn from specified probability distribution
Alt. Hypothesis:
Sample was not drawn from specified probability distribution

Bins:                    10
Distribution:            ChiSquare(9)
Computed statistic:      156.086
Computed pvalue:         0
Critical value:          16.9189774487099

Result: [Rejected]
There exists statistical evidence against the null hypothesis

Kanju, Gopal K. 100 Statistical Tests. London: SAGE Publications Ltd., 1994.

Sheskin, David J. Handbook of Parametric and Nonparametric Statistical Procedures. London: CRC Press, 1997.