Manuals/calci/GAMMADIST

GAMMADIST(x,alpha,beta,cu)

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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha & \beta} .
In GAMMADIST(x,alpha,beta,cu), 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.
The gamma function is defined by :

.

And it is for all complex numbers except the negative integers and zero.
The probability density function of Gamma function using Shape, rate parameters is: f(x; α,ß)=[x^{α-1} e^-{x/ß}]/ß^α Gamma(α), for x,α &ß>0, where e is the natural number(e=2.71828...), α is the number of occurrences of an event, and Gamma(α) is the Gamma function.
The standard gamma probability density function is: f(x, α)=[x^{α-1} e^-x]/Gamma(α).
The cumulative distribution function of Gamma is F(x;α,ß)=[Gamma(in symbol V)(α, x/ß)]/Gamma(α), or F(x;α,ß)= e^-{x/ß} Summation i=k to infinity 1/i! (x/ß)^i for any positive integer k.
When alpha is a positive integer, then the distribution is called Erlang distribution.
If the shape parameter α is held fixed, the resulting one-parameter family of distributions is a natural exponential family.
For a positive integer n, when alpha = n/2, beta = 2, and cu= TRUE, GAMMADIST returns (1 - CHIDIST(x)) with n degrees of freedom.
This function shows the result as error when 1.Any one of the argument is non numeric

2. x<0, alpha<=0 or beta<=0