Discussion
A frequency data is classified in 9 classes and Gamma distribution is fitted to it after estimating the parameters. If a \(\chi^{2}\) goodness of fit test is to be used without combining the classes, the degrees of freedom associated with \(\chi^{2}\) test are :
Answer: D
The degrees of freedom are 6.
For a chi-square goodness-of-fit test with \(k\) classes and \(s\) parameters estimated from the data,
\[ \nu = k - 1 - s = 9 - 1 - 2 = 6 \]
One degree of freedom is lost because the expected frequencies are made to total the observed total, and one more for each estimated parameter; the gamma distribution has two (shape and scale).
9 forgets every restriction, 8 subtracts only the total, and 7 counts only one estimated parameter.
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