Difference between revisions of "Manuals/calci/GAMMAINV"

Revision as of 04:28, 4 December 2013

GAMMAINV(prob,alpha,beta)

This function gives the inverse value of Cumulative Gamma Probability Distribution.
This distribution is the Continuous Probability Distribution on the positive real line and it is of the reciprocal of a variable distributed according to the gamma distribution with two parameters $\alpha$ & $\beta$ .
It is used in Bayesian statistics.
In $GAMMAINV(prob,\alpha ,\beta )$ , $prob$ is the probability value associated with Gamma Distribution, $\alpha$ is called shape parameter and $beta$ is the rate parameter of the distribution.
If $GAMMADIST(x,alpha,beta,TRUE)=prob$ , then $GAMMAINV(prob,alpha,beta,)=x$ .
GAMMAINV use the iterating method to find the value of $x$ .
Suppose the iteration has not converged after 100 searches, then the function gives the error result.
This function will give the error result when

1.Any one of the arguments are non-numeric
2. $\alpha \leq 0$  or  $\beta \leq 0$ 
3. $prob<0$  or  $prob>1$

=GAMMAINV(0.65189,2,5) = 11.1335534510
=GAMMAINV(0.006867292,5,7) = 8.155481331
=GAMMAINV(0.1543869,9,3) = 18.0467153645
=GAMMAINV(1,9,3) = 82.51739521528073
=GAMMAINV(1.1,9,3) = NAN, because $prob>1$

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 <div style="font-size:30px">'''GAMMAINV(prob,alpha,beta)'''</div><br/>
 *<math>prob</math> is the probability value associated with gamma distribution
-*<math>alpha</math>& <math>beta</math> are the values of  the shape and rate parameters
+*<math>alpha</math> & <math>beta</math> are the values of  the shape and rate parameters
 ==Description==
 *This function gives the inverse value of Cumulative Gamma Probability Distribution.