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.

* Complete program (with open source codes) available in Package Set 2 and the Combo Package.