The Student’s t distribution is continuous. It is used to describe small sets of empirical data that resemble a normal curve, but with thicker tails (more outliers). It is often used for econometric data and exchange rates.
Midpoint, Scale, Degrees of Freedom
The Midpoint parameter is the central location of the distribution (also mode), the x-axis value where you want to place the peak of the distribution. The Degrees of Freedom parameter controls the shape of the distribution. Smaller values result in thicker tails and less mass in the center. The Scale parameter affects the width of the distribution by increasing the variance without affecting the overall shape and proportions of the curve. Scale can be used to widen the curve for easier reading and interpretation. For example, if the midpoint were a large number, say 5000, the scale could be proportionately larger than if the midpoint were 500. |
The Student’s t distribution is used under these conditions:
Note: | When degrees of freedom are greater than 30, the normal distribution can be used to approximate the Student's t distribution. |
For examples, see Normal Distribution. The uses are the same except that the sample degrees of freedom will be < 30 for the Student’s t distribution.