In MS Excel, Gamma distribution can be easily calculated by using GAMMA.DIST function. This function is available from MS Excel 2010 onwards. For previous version there is GAMMADIST function (without a dot between).

Function Details

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

 

Arguments of Function

  • X (Required)– The value at which gamma function would be evaluated
  • Alpha / α (Required) – A parameter of the distribution used for determining the shape.
  • beta / β (Required) – A parameter of the distribution for determining the rate

α and β are both must be greater than 1.

When α = 1, it corresponds to exponential distribution.

When β = 1, it corresponds to the standard gamma distribution.

• Cumulative (Required) - A logical value that determines the form of the function.

Cumulative =TRUE, it returns the cumulative distribution function

Cumulative =FALSE, it returns the probability density function.

 

Stepwise Execution

Go to an empty cell and type =GAMMA.DIST

function

  1. Type the value where we need to find probability. This gives us the value of x. In the example below, x= 5
  2. Type the alpha and beta value as the next parameters, both comma separated. Here, α = 4 & β = 3
  3. Type True for cumulative distribution. Type False for probability density function.

 

 

Formula & Result

=GAMMA.DIST(5, 4, 3, TRUE)

 

Result: 0.088267

=GAMMA.DIST(5, 4, 3, False)

Result: 0.048579

 

Graph Generation Cumulative Distribution function (CDF) and Probability Density Function (PDF)

Take time T = 0 - n. In the example, time is taken from 0 to 20. Here value of T = value of x

time

Fix values for α = 4 & β = 3

alpha and beta

 

Cumulative Distribution function (CDF)

Formula: =GAMMA.DIST(D16, 4, 3, TRUE)

Probability Density function (PDF)

Formula: =GAMMA.DIST(D16, 4, 3, FALSE)

Cumulative Distribution function CDF and Probability Density function PDF

Cumulative Distribution function 

Probability Density function

 

Errors

  • #NUM! – Occurs under following scenarios:

Value of x < 0

Value of α ≤ 0 or β ≤ 0

  • #VALUE! – Occurs under following scenarios:

Any of the arguments – x, alpha, beta are non-numeric in nature

The fourth parameter is not TRUE OR FALSE, unrecognized

Further reading: 
Distribution chart