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STATLECT > Probability distributions > Gamma distribution

Plots of the Gamma distribution

This page collects some plots of the Gamma distribution. The plots help us to understand how the shape of the Gamma distribution changes when its parameters are changed.

Density plots

The following plot contains the graphs of two Gamma probability density functions. The first graph (blue line) is the probability density function of a Gamma random variable with $n=1$ degrees of freedom and mean $h=2$. The second graph (red line) is the probability density function of a Gamma random variable with $n=5$ degrees of freedom and mean $h=2$. As $h=2$ in both cases, the two distributions have the same mean. However, increasing the number of degrees of freedom from $n=1$ to $n=5$ changes the shape of the distribution (the more the degrees of freedom are increased the more the distribution resembles a normal distribution). The thin vertical lines indicate the means of the two distributions.

Gamma density plot 1

The following plot contains the graphs of two Gamma probability density functions. The first graph (blue line) is the probability density function of a Gamma random variable with $n=6$ degrees of freedom and mean $h=3$. The second graph (red line) is the probability density function of a Gamma random variable with $n=8$ degrees of freedom and mean $h=3$. As $h=3$ in both cases, the two distributions have the same mean. However, increasing the number of degrees of freedom from $n=6$ to $n=8$ changes the shape of the distribution (the more the degrees of freedom are increased the more the distribution resembles a normal distribution). The thin vertical lines indicate the means of the two distributions.

Gamma density plot 2

The following plot contains the graphs of two Gamma probability density functions. The first graph (blue line) is the probability density function of a Gamma random variable with $n=3$ degrees of freedom and mean $h=2$. The second graph (red line) is the probability density function of a Gamma random variable with $n=3$ degrees of freedom and mean $h=4$. Increasing the parameter $h$ changes the mean of the distribution (from $2$ to $4$). However, the two distributions have the same number of degrees of freedom ($n=3$). Therefore, they have the same shape (one is the 'stretched version of the other' - it would look exactly the same on a different scale). The thin vertical lines indicate the means of the two distributions.

Gamma density plot 3

The following plot contains the graphs of two Gamma probability density functions. The first graph (blue line) is the probability density function of a Gamma random variable with $n=6$ degrees of freedom and mean $h=2$. The second graph (red line) is the probability density function of a Gamma random variable with $n=6$ degrees of freedom and mean $h=4$. Increasing the parameter $h$ changes the mean of the distribution (from $2$ to $4$). However, the two distributions have the same number of degrees of freedom ($n=6$). Therefore, they have the same shape (one is the 'stretched version of the other' - it would look exactly the same on a different scale). The thin vertical lines indicate the means of the two distributions.

Gamma density plot 4

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