Manuals/calci/GAMMADIST
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GAMMADIST(x,alpha,beta,cu)
- Where 'x' is the value of the distribution,'alpha' and 'beta' are the value of the parameters and '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 α&ß.
- 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 it is TRUE then this function gives the cumulative distribution value or it is FALSE then it gives the probability density function.
- The gamma function is defined by Gamma(t) = integral 0 to infinity 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