Retrieving table values from a ChiSquareDistribution function

Questions
1

Hi;

I am attempting to retrieve the ChiSquare values from the ChiSquareDistribution (as opposed to a paper table) to perform the following calculations, please see attached notebook. In trying to retrieve the values, I have tried several different flavors of the CDF function without success. Additionally, I have read the documentation, and it is not real clear.

I would appreciate any help.

Thanks,

Mitch Sandlin

ChiSquareQuestion.nb (61.7 KB)

2

What you have labeled \chi^2_{\alpha/2}\approx 26.119 is the value of a chisquare random variable X that has a probability of \alpha/2 in the right tail. The correct function to use is the InverseCDF which gives the value of the chisquare random variable that has \alpha/2 in the left tail. So you will need the following:

InverseCDF[ChiSquareDistribution[14], 0.05/2]
(* 5.62873 *)
InverseCDF[ChiSquareDistribution[14], 1 - 0.05/2]
(* 26.1189 *)

You get the wrong value because in your attachment you have

CDF[ChiSquareDistribution[14], (1 - 0.05)/2]

which should be

InverseCDF[ChiSquareDistribution[14], 1 - 0.05/2]
3

Hi Jim and thanks so much.

Would using the Variable function (Variable[ChiSquareDistribution[v]]) be a better option since calculating the variance is my Gold? However, I am not sure how to load the parameters of this function, and since there is only one (which is associated with the ChiSquareDistribution function), I am assuming that it (v) would be used for the degrees of freedom. So how would I load the Alpha values?

It appears that the Mean function (Mean[ChiSquareDistribution[v]]) has the same sort of ambiguity in documentation.

Thanks again,

Mitch Sandlin