Random Number Generator - Student-t Distribution

Student¡¦s t distribution is used commonly for small sample size -usually a sample size less than 30. A t distribution shares some common characteristics with the standard normal distribution. Both distributions are symmetrical, both range in value from negative infinity to positive infinity, and both have a mean of zero and standard derivation of one. However, a t distribution has a greater dispersion than the standard normal distribution.

The following example shows input and output from 3 simulations. Each has the degree of freedom of 5,10, and 30 respectively. All three simulations have 10,000 iterations and alpha of 5% (for 1 tail test).

The output shows the estimate of skewness, mean, stand deviation, maximum value, minimum value, lower confidence interval, and upper confidence interval from each of the 3 simulations. As the degree of freedom (sample size - 1) decreases from simulation 1 to simulation 3, the standard deviation approaches to 1. The mean remains close to zero through all 3 simulations.

The following three charts show as degree of freedom increases, the distribution approaches to normal.