Part 2. MM4XL Tools > 1. Strategic Tools > Risk Analyst > 4. Functions > 3. Distribution Functions > mmGAMMA(Scale, Shape)

## Risk Analyst

### mmGAMMA(Scale, Shape)

Example

=mmGAMMA(2, 1) can equal 2.073131782

#### Application

This function is typically used to study variables that may have a skewed distribution and whose outcome is not completely random. It can model the time elapsing between events, and it is commonly used in inventory control and queuing analysis.

In many cases, this kind of event can also be modeled with mmNORMAL. The drawback is that mmNORMAL accounts for negative numbers too and it is symmetrical. When it is desirable to work with a positive, right skewed distribution the mmGAMMA or the mmLOGNORMAL can help. The Gamma function is less skewed than the Lognormal, so it assigns lower probability to extreme values.

#### How to use

This function returns the amount of time between events. Say, we are modeling the time to issue an order to restock the inventory of sodas at a retail store. The order can be issued only when all 3 brands of soda that the store carries have one or zero units in stock. From historical data we know this happens every 28 days plus or minus 7 days. The formula below may be used to simulate the time in days to reorder sodas:

=mmGAMMA(7, 4)

Copy the formula above in 100 cells. You will find the simulated values ranging from 0 to 70 days, and the mean is centered around 28 days (the mean of the mmGAMMA is found by multiplying the Scale times Shape parameters 7 times 4 in our example equals 28 days to reorder sodas).

#### Technical profile

 Type Continuous distribution. Syntax =mmGAMMA(Scale, Shape) Domain ; generates positive numbers only. Mode If Scale >= 1 then Shape(Scale-1) If Scale < 1 then = 0 Parameters Scale = b > 0 Shape = c > 0 Remarks If any argument is nonnumeric mmGAMMA returns the #VALUE! error value. Relationships When Shape is an integer the distribution function is the same as that of the Erlang distribution. It is related to the Chi2 distribution. Graphs mmGAMMA(2, 1) mmGAMMA(20, 10)  Lifetime license:
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