   7.5.4  Testing a distribution with the χ2 distribution: chisquaret

The chisquaret command will use the χ2 test to compare sample data to a specified distribution. You need to provide chisquaret with the following arguments:

1. A list of sample data.
2. The name of a distribution, or another list of sample data. If this is omitted, a uniform distribution will be used.
3. The parameters of the distribution, if a name is given as the previous argument, or the parameter class followed by class_min and class_dim (or the default values will be used).

The chisquaret command will return the result of the χ2 test between the sample data and the named distribution or the two sample data.

For example, if you enter

chisquaret([57,54])

you will get

```  Guessing data is the list of number of elements in each class,
Sample adequation to a finite discrete probability distribution
Chi2 test result 0.0810810810811,
reject adequation if superior to chisquare_icdf(1,0.95)=3.84145882069 or chisquare_icdf(1,1-alpha) if alpha!=5%
0.0810810810811
```

If you enter

chisquaret([1,1,1,1,1,0,0,1,0,1,1],[.4,.6])

you will get

```   Sample adequation to a finite discrete probability distribution
Chi2 test result 0.742424242424,
reject adequation if superior to chisquare_icdf(1,0.95)=3.84145882069
or chisquare_icdf(1,1-alpha) if alpha!=5%
0.742424242424
```

If you enter

chisquaret(ranv(1000,binomial,10,.5),binomial)

you will get

```   Binomial: estimating n and p from data 10 0.5055
Sample adequation to binomial(10,0.5055,.), Chi2 test result 7.77825189838,
reject adequation if superior to chisquare_icdf(7,0.95)=14.0671404493
or chisquare_icdf(7,1-alpha) if alpha!=5%
7.77825189838
```

and if you enter

chisquaret(ranv(1000,binomial,10,.5),binomial,11,.5)

you will get

```   Sample adequation to binomial(11,0.5,.), Chi2 test result 125.617374161,
reject adequation if superior to chisquare_icdf(10,0.95)=18.3070380533
or chisquare_icdf(10,1-alpha) if alpha!=5%
125.617374161
```

For an example using class_min and class_dim, let

L := ranv(1000,normald,0,.2)

If you then enter

chisquaret(L,normald,classes,-2,.25)

or equivalently set class_min to −2 and class_dim to −0.25 in the graphical configuration and enter

chisquaret(L,normald,classes)

you will get

```   Normal density,
estimating mean and stddev from data -0.00345919752912 0.201708100832   