Part 2. MM4XL Tools > 1. Strategic Tools > Risk Analyst > 4. Functions > 3. Distribution Functions > mmSTUDENT(Degrees)

Risk Analyst



=mmSTUDENT(6) can equal 0.750778794.


Also called the Students t, this is a distribution used to model events for which we have a mean but not a standard deviation (as in most cases). It could be blood pressure, amplitude of noise, financial returns during normal times, small samples arising in statistical quality control, and more.

It is bell-shaped with peak at zero like the Normal distribution. However, the spread of values around the mean is heavier than that of the Normal distribution, which means the Student distribution attributes more probability to extreme values than the Normal distribution does. As the degrees of freedom get large, the t distribution gets closer to the standard normal distribution. When the degrees of freedom are more than 30 the Normal approximates the Student distribution. In a way, we can think of the Normal distribution as a special case of the t-distribution appropriate when sample sizes are large.

How to use

Say we are modeling the weight of biscuit boxes. In order to measure the accuracy of production, we select 15 boxes from each production lot and measure an average weight of 720 grams with standard deviation equal to 25 grams. The formula below produces t values that can be used to simulate box weights. It is a two-step process. Step 1: the formula below produces a t value:


Step 2: the obtained t value is used within the TDIST function, built in to MS Excel, in order to simulate the average box weight. If this falls outside certain limits it could require the production supervision to reject the box, and rejections produce costs that management dislikes. The following formula returns weight in the range 720 plus or minus 25, according to the t distribution:


Technical profile

Type Continuous distribution.
Syntax =mmSTUDENT(Degrees)
Domain  Monte Carlo Simulation Software: Management Process Risk Analysis
Mode 0.
Parameters Degrees = v > 0, an integer = Sample size 1
Remarks If Degrees is nonnumeric mmSTUDENT returns the #VALUE! error value.
Relationships It is related to the Chi2 and to the Normal variate.
 Monte Carlo Simulation Software: Management Process Risk Analysis  Monte Carlo Simulation Software: Management Process Risk Analysis
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