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 (syntax error): {\displaystyle \alpha & \beta} .
In GAMMADIST(x,alpha,beta,cu), $x$ is the value of the distribution, $\alpha$ is called shape parameter and $beta$ is the rate parameter of the distribution and $cu$ is the logical value like TRUE or FALSE.
If $cu$ 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 :

$Gamma(t)=\int \limits _{0}^{\infty }x^{t-1}e^{-x}dx$ .

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