Manuals/calci/GAMMADIST
- 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} is the value of the distribution,
- 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'} and 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 'beta'} are the value of the 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 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 (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), 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} is the value of the distribution, 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} is called shape parameter and 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 beta} is the rate parameter of the distribution and 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 cu} is the logical value like TRUE or FALSE.
- If 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 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 :
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 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 <math>x,\alpha & \beta > 0 } , where 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 e} is the natural number(e = 2.71828...), 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} is the number of occurrences of an event, and 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 Gamma(\alpha)} is the Gamma function.
- The standard Gamma Probability Density function is:
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)=\frac{x^{\alpha-1} e^{-x}}{Gamma(\alpha)}} .
- The Cumulative Distribution Function of Gamma is 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)=[\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 .
- 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