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STATLECT > Probability distributions > F distribution

Plots of the F distribution

This page collects some plots of the F distribution. The plots help us to understand how the shape of the distribution changes when a parameter is changed.

Density plots

The following plot contains the graphs of two F probability density functions. The first graph (blue line) is the probability density function of an F random variable with parameters $n_{1}=4$ and $n_{2}=4$. The second graph (red line) is the probability density function of an F random variable with parameters $n_{1}=20$ and $n_{2}=4$. Increasing the first parameter from $n_{1}=4$ to $n_{1}=20$, the mean of the distribution (represented by the vertical line in the graph) does not change, however density is shifted from the tails to the center of the distribution.

F density plot 1

The following plot contains the graphs of two F probability density functions. The first graph (blue line) is the probability density function of an F random variable with parameters $n_{1}=4$ and $n_{2}=4$. The second graph (red line) is the probability density function of an F random variable with parameters $n_{1}=4$ and $n_{2}=20$. Increasing the second parameter from $n_{2}=4$ to $n_{2}=20$, the mean of the distribution (represented by the vertical line in the graph) decreases (from $2$ to $ rac{10}{9}$) and density is shifted from the tails (mostly from the right tail) to the center of the distribution.

F density plot 2

The following plot contains the graphs of two F probability density functions. The first graph (blue line) is the probability density function of an F random variable with parameters $n_{1}=4$ and $n_{2}=4$. The second graph (red line) is the probability density function of an F random variable with parameters $n_{1}=20$ and $n_{2}=20$. Increasing the two parameters, the mean of the distribution (represented by the vertical line in the graph) decreases (from $2$ to $ rac{10}{9}$) and density is shifted from the tails to the center of the distribution. As a result, the distribution takes a bell shape similar to the shape of the normal distribution.

F density plot 3

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