Manuals/calci/GAMMADIST

GAMMADIST(x,alpha,beta,cu)

• $x$ is the value of the distribution,
• $'alpha'$ and $'beta'$ are the value of the parameters
• $cu$ is the logical value like true or false.

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 :

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

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

Failed to parse (syntax error): {\displaystyle f(x; \alpha,\beta)=\frac{x^{\alpha-1} e^-{\frac {x}{\beta}}{\beta^{\alpha} Gamma(\alpha)}} , for 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 x,\alpha & \beta > 0 } , where $e$ is the natural number(e = 2.71828...), $\alpha$ is the number of occurrences of an event, and $Gamma(\alpha )$ is the Gamma function.

• The standard Gamma Probability Density function is:

$f(x,\alpha )={\frac {x^{\alpha -1}e^{-x}}{Gamma(\alpha )}}$.

• The Cumulative Distribution Function of Gamma is Failed to parse (syntax error): {\displaystyle F(x;\alpha,\beta)=[\gamma(\alpha,\frac{x}{\beta}}{Gamma(\alpha)}} , or 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 F(x;\alpha,\beta)= e^-{\frac {x}{\beta}} \sum_{i=k}^{\infty}\frac{1}{i!}{\frac{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

See Also

• DATE
• DAYS360
• DATEVALUE

References

Bessel Function