# Manuals/calci/GAMMADIST

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**GAMMADIST(x,alpha,beta,cumulative,accuracy)**

- is the value of the distribution.
- and are the value of the parameters.
- is the logical value like true or false.
- gives accurate value of the solution.
- GAMMADIST(), returns the gamma distribution.

## Description

- This function gives the value of the Gamma Distribution.
- The Gamma Distribution can be used in a queuing models like, the amount of rainfall accumulated in a reservoir.
- This distribution is the Continuous Probability Distribution with two parameters and .
- In , is the value of the distribution, is called shape parameter and is the rate parameter of the distribution and is the logical value like TRUE or FALSE.
- If is TRUE, then this function gives the Cumulative Distribution value and if is FALSE then it gives the Probability Density Function.
- gives accurate value of the solution.
- The gamma function is defined by :

.

- It is for all complex numbers except the negative integers and zero.
- The Probability Density Function of Gamma function using Shape, rate parameters is:

, for

- , where is the natural number(e = 2.71828...), is the number of occurrences of an event, and is the Gamma function.

- The Standard Gamma Probability Density function is:

.

- The Cumulative Distribution Function of Gamma is :

, or

- for any positive integer .

- When alpha is a positive integer, then the distribution is called Erlang distribution.
- If the shape parameter is held fixed, the resulting one-parameter family of distributions is a natural exponential family.
- For a positive integer , when , , and , GAMMADIST returns (1 - CHIDIST(x)) with degrees of freedom.
- This function shows the result as error when

1.Any one of the argument is non numeric 2., or .

## ZOS

- The syntax is to calculate GAMMADIST in ZOS is .
- is the value of the distribution,
- and are the value of the parameters
- is the logical value like true or false.
- gives accurate value of the solution.

- For e.g.,GAMMADIST(10.45,2.8,6.4,TRUE,0.9)

GAMMADIST(10.45,2.8,6.4,FALSE,0.9)

## Examples

- GAMMADIST(8.15372,5,7,TRUE)=0.006867292
- GAMMADIST(20.78542,2,6,TRUE)=0.860283293
- GAMMADIST(20.78542,2,6,FALSE)=0.01806997
- GAMMADIST(45.6523,9,4,FALSE)=0.019724471
- GAMMADIST(8.15372,5,7,TRUE,0.5)= 0.00693316259
- GAMMADIST(8.15372,5,7,TRUE,0.9)=0.0067648564

## Related Videos

## See Also

## References