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STATLECT > Probability distributions > Student's t distribution

Plots of the Student's t distribution

This page collects some plots of the Student's t 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 Student's t probability density functions. The first graph (blue line) is the probability density function of a Student's t random variable with parameters $mu =0$, $\sigma =1$ and $n=5$. The second graph (red line) is the probability density function of a Student's t random variable with parameters $mu =1$, $\sigma =1$ and $n=5$. Changing the mean from $mu =0$ to $mu =1$, the shape of the graph does not change, but the graph is translated to the right (its location changes).

Student's t density plot 1

The following plot contains the graphs of two Student's t probability density functions. The first graph (blue line) is the probability density function of a Student's t random variable with parameters $mu =0$, $sigma =1$ and $n=5$. The second graph (red line) is the probability density function of a Student's t random variable with parameters $mu =0$, $sigma =2$ and $n=5$. Changing the scale parameter from $sigma =1$ to $sigma =2$, the location of the graph does not change (it remains centered at 0), but the shape of the graph changes (there is less density in the center and more density in the tails).

Student's t density plot 2

The following plot contains the graphs of two Student's t probability density functions. The first graph (blue line) is the probability density function of a Student's t random variable with parameters $mu =0$, $\sigma =1$ and $n=5$. The second graph (red line) is the probability density function of a Student's t random variable with parameters $mu =0$, $\sigma =1$ and $n=25$. Increasing the number of degrees of freedom from $n=5$ to $n=25$, the location of the graph does not change (it remains centered at 0) and its shape changes only marginally (the tails become thinner).

Student's t density plot 3

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