t-Distribution Random Generator
Generate random numbers from a Student t-distribution with a chosen degrees of freedom. Shows the list, a histogram, and sample mean and standard deviation.
Input
Enter the degrees of freedom nu and how many values to draw, then press the button to generate random numbers from a Student t-distribution.
df
Enter a value greater than 0.
values
From 1 to 100000.
Result
Enter the degrees of freedom and a count, then press generate.
How it works
- A t random value with degrees of freedom nu is built from a standard normal Z and a chi-square value C with nu degrees of freedom as T = Z divided by the square root of C over nu.
- The standard normal values use the Box-Muller method, and the chi-square value is the sum of squared standard normal values.
- As the degrees of freedom grow, the distribution approaches the standard normal distribution; smaller values give heavier tails.
- Random numbers are generated the moment you press the button, and each press gives a different result.
- The sample mean and sample standard deviation are measured from the generated values and differ from the theoretical values.
- When the degrees of freedom nu is 2 or less the population variance is not finite, so the sample standard deviation swings widely between runs.
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t-Distribution Random Generator