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#Statistical

GAMMA.INV

Excel Functions

Get inverse of gamma cumulative distribution

Syntax

EXCEL 
=GAMMA.INV(probability, alpha, beta)

Arguments

Parameter Description
probability The probability associated with the gamma distribution (must be between 0 and 1).
alpha The shape parameter of the distribution.
beta The scale parameter of the distribution.

Return Value

Threshold value of a probability

Details

GAMMA.INV is used to find the value at which the cumulative gamma distribution reaches a specified probability. In other words, it answers the question: "For a given probability, what is the corresponding value of x in the gamma distribution?" This is also known as the quantile or percentile function. Suppose you work at a stall at the farmers' market. Customers appear one at a time, at random, but historical data tell you they arrive on average 10 per hour. You want to know the maximum time you would have to wait for the 20th customer to show up, such that there is a 90% chance the 20th customer will have arrived by that time. To set up the problem as a gamma distribution: To find the time by which there is a 90% chance the 20th customer will have arrived: This means there is a 90% chance

Examples

Example #1 - Find a waiting time threshold

To find the time by which there is a 90% chance the 20th customer will have arrived:

EXCEL 
=GAMMA.INV(0.9, 20, 0.1) // returns 2.590252861
Example #2 - Relationship to GAMMA.DIST

GAMMA.INV is the inverse of GAMMA.DIST with cumulative = TRUE. For example, using the result from above, you can check the probability of the 20th cus

EXCEL 
=GAMMA.DIST(2.590252861, 20, 0.1, TRUE) // returns 0.9
Example #3 - Calculate value at percentile

In general, you can use GAMMA.INV to find the value at the percentile of a gamma distribution. For example, to find the value at the 25th, 50th, and 7

EXCEL 
=GAMMA.INV(0.25, 20, 0.1) // returns 1.683014746
=GAMMA.INV(0.50, 20, 0.1) // returns 1.966767242
=GAMMA.INV(0.75, 20, 0.1) // returns 2.280800681

See Also

GAMMA.DIST