Difference between revisions of "Manuals/calci/GAMMADIST"
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(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> <font color="#000000">'''GAMMADIST(X, Alpha, Beta, Cum)'''</font> <br /> <font color="#000000">Where X is the...") |
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| − | <div | + | <div style="font-size:30px">'''GAMMADIST(x,alpha,beta,cu)'''</div><br/> |
| + | *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 | ||
| + | ==Examples== | ||
| − | + | #EDATE("1/1/1910",2)=Tue Mar 01 1910 00:00:00 GMT +0530 (Indian standard time) | |
| + | #EDATE("5/4/1897",5)=Mon Tue 04 189700:00:00 GMT +0530 (Indian standard time) | ||
| + | #EDATE("11/31/1999",3)=Wed Mar 01 200000:00:00 GMT +0530 (Indian standard time) | ||
| + | #EDATE("6/6/1979",-2)=Fri Apr 06 197900:00:00 GMT +0530 (Indian standard time) | ||
| + | #EDATE("4/15/1950",-6)=Sat Oct 15 194900:00:00 GMT +0530 (Indian standard time) | ||
| + | ==See Also== | ||
| + | *[[Manuals/calci/DATE | DATE ]] | ||
| + | *[[Manuals/calci/DAYS360 | DAYS360]] | ||
| + | *[[Manuals/calci/DATEVALUE | DATEVALUE]] | ||
| − | + | ==References== | |
| − | + | [http://en.wikipedia.org/wiki/Bessel_function| Bessel Function] | |
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Revision as of 05:17, 3 December 2013
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
Examples
- EDATE("1/1/1910",2)=Tue Mar 01 1910 00:00:00 GMT +0530 (Indian standard time)
- EDATE("5/4/1897",5)=Mon Tue 04 189700:00:00 GMT +0530 (Indian standard time)
- EDATE("11/31/1999",3)=Wed Mar 01 200000:00:00 GMT +0530 (Indian standard time)
- EDATE("6/6/1979",-2)=Fri Apr 06 197900:00:00 GMT +0530 (Indian standard time)
- EDATE("4/15/1950",-6)=Sat Oct 15 194900:00:00 GMT +0530 (Indian standard time)