GAMMA.DIST

Calculates the gamma distribution.

Syntax:

GAMMA.DIST(x, alpha, beta, cumulative)

x is required, and is the value you want to use to evaluate the distribution.

alpha is required, and is the shape parameter of the gamma distribution (must be greater than 0).

beta is the scale parameter of the gamma distribution (must be greater than 0).

cumulative is required, and is a logical value:

TRUE: Returns the cumulative distribution function (the probability that a random variable is less than or equal to x).

FALSE: Returns the probability density function (the height of the gamma distribution curve at x).

Example:

If x contains 3, alpha contains 2, beta contains 1.5 and cumulative contains FALSE:

GAMMA.DIST(3, 2, 1.5, FALSE)

returns 0.180447044

x:

Alpha:

Beta:

Cumulative:

Result:

0.180447044

Application:

Scenario:

Imagine a call center manager wants to analyze the probability of receiving the 10th call within a certain amount of time. Based on historical data, the average time between calls (the mean waiting time) is 0.5 minutes.

To model this, we use the gamma distribution with the following parameters:

Shape (alpha): The number of events to occur. In this case, alpha=10.
Scale (beta): The mean waiting time between events. In this case, beta=0.5 minutes.
Time (x): The specific time value for which we want to find the probability.

The GAMMA.DIST function calculates the cumulative probability that the 10th call will arrive at or before time x.

Results Table:

The table below shows the probability of the 10th call arriving within a given number of minutes.

	Time (minutes)	Probability (CDF)
	A	B
1	1	0%
2	2	0.81%
3	3	8.39%
4	4	28.34%
5	5	54.21%
6	6	75.76%
7	7	89.06%
8	8	95.67%
9	9	98.46%
10	10	99.5%

Interpretation:

The table shows that:

There is a very low chance (less than 1%) of the 10th call arriving within 2 minutes.
The probability increases significantly as time goes on. For example, there is a 54.21% chance that the 10th call will arrive within 5 minutes.
There is a high probability (99.50%) that the 10th call will be received within 10 minutes.

This kind of analysis helps the manager optimize staffing levels and better predict call volumes to ensure efficient customer service.