# Questions tagged [f-distribution]

The F distribution is a continuous probability distribution which is commonly used in statistical testing procedures.

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### Sum of two i.i.d R.V having singly non-central F distribution

Noncentral F-distribution is used frequently in communication areas. In one of the applications, I need to do a sum of two i.i.d R.V having non-central F-distribution with parameter 1 (d.o.f for ...
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### Derivation of F distribution from quotient distribution

I'm looking for the derivation of the F distribution. There is a fairly understandable (for me) derivation presented on this site: http://www.milefoot.com/math/stat/pdfc-fdist.htm. On this site, the ...
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### Compounding Gamma with Gamma to yield F-distribution?

I am working through some problems from my Bayesian Statistics course and am having trouble understanding a step in the solution to a question. For reference this is the question: And here is the ...
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### What is $F_{k,\infty}$, i.e., $F$ distribution when the second degree of freedom approaches infinity?

What is $F_{k,\infty}$, i.e., $F$ distribution when the second degree of freedom approaches infinity? I'm wondering if there is a known distribution(such as $\chi_k^2$) that it converges to.
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1 vote
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### Does X^2 divided to DF converge to F distribution when X^2 is Rao Scott chi squared statistic?

I'm studying Rao-Scott chi-squared test, kind of survey sampling analysis method. It uses when we want to test independence between two variables under complex sampling data instead of Pearson chi-...
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### From expected value of R2 in Regression to expected value of partial eta squared in ANOVA

In general, $R^2$, the estimator of "multiple correlation coefficient" in regression, is known to be positively biased. Given $K$ predictors, and $N$ total sample size, Johnson, Kotz, & ...
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### Derive the distribution of the ANOVA F-statistic under the alternative hypothesis

Say we have $k$ samples of data, where sample $i$ is of size $n_i$ and we write it as $x_{i1}, ... , x_{in_i}$. Let the total sample size be $N$. The ANOVA model is $X_{ij} \sim N(\mu_i, \sigma^2)$ ...
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1 vote
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### How does one calculate the F-value-threshold used to evaluate an F-test?

I am studying Response Surface Methodology (by Myers, Montgomery, and Anderson-Cook). When introducing the significance testing for regression parameters, an $F$-test is introduced but only partially ...
1 vote
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### Can you perform an inverse F-test on two datasets with the same degrees of freedom?

Stats newbie here. Is there any meaning to the critical F value if the two samples have the same degrees of freedom? For example, I have 2 sets of data, each with the same number of degrees of ...
Suppose that $X \sim F(n,n)$, an F distribution on $n$ and $n$ degrees of freedom. I'm trying to figure out why some literature state that $X$ converges in distribution to a normal distribution. My ...