Manuals/calci/GAMMADIST

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

See Also

• DATE
• DAYS360
• DATEVALUE

References

Bessel Function