Manuals/calci/BETAINV

BETAINV (Probability,Alpha,Beta,LowerBound,UpperBound,Accuracy,DivisionsAndDepthArray)

• $Probability$ is the probability value associated with the beta distribution.
• $Alpha$ & $Beta$ are the values of the shape parameter.
• $LowerBound$ & $UpperBound$ the lower and upper limit to the interval of $x$.
• $Accuracy$ gives accurate value of the solution.
• $DivisionsAndDepthArray$ is the value of the division.
  • BETAINV(), returns the inverse of the Cumulative Distribution Function for a specified beta distribution.

Description

• This function gives the inverse value of Cumulative Beta Probability Distribution.
• It is called Inverted Beta Function or Beta Prime.
• In $BETAINV(Probability,Alpha,Beta,LowerBound,UpperBound,Accuracy,DivisionsAndDepthArray)$, $Probability$ is the probability value associated with Beta Distribution, $Alpha$ and $Beta$ are the values of two positive shape parameters and $LowerBound$ and $UpperBound$ are the lower and upper limit.
• Normally the limit values are optional, i.e. when we are giving the values of $LowerBound$&$UpperBound$ then the result value is from $a$ and $b$.
• When we are omitting the values $LowerBound$ and $UpperBound$, by default it will consider $LowerBound=0$ and $UpperBound=1$, so the result value is from $0$ and $1$.
• If $BETADIST(Number,Alpha,Beta,LowerBound,UpperBound)=Probability$, then $BETAINV(Probability,Alpha,Beta,LowerBound,UpperBound,Accuracy,DivisionsAndDepthArray)=x$.
• $BETAINV$ 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 or Beta $\leq$ 0 
3.Number<LowerBound ,Number>UpperBound or LowerBound = UpperBound
4.we are not mentioning the limit values  for LowerBound & UpperBound , 
  by default it will consider the Standard Cumulative Beta Distribution, LowerBound = 0 and UpperBound = 1

ZOS

• The syntax is to calculate of this function in ZOS is $BETAINV(Probability,Alpha,Beta,LowerBound,UpperBound,Accuracy,DivisionsAndDepthArray)$.
  • $probability$ is the probability value associated with the beta distribution.
  • $Alpha$ and $Beta$ are the values of the shape parameter.
  • For e.g.,BETAINV(0.30987,10,18,12,16)

Examples

1. BETAINV(0.2060381025,5,9,2,6) = 3
2. BETAINV(0.359492343,8,10) = 1.75
3. BETAINV(0.685470581,5,8,2,6) = 3.75
4. BETAINV(0.75267,1,7,7,9) = 7.25
5. BETAINV(0.5689,-2,4,3,5) = NAN, because $\alpha <0$.

Related Videos

Beta Inverse Distribution

See Also

• BETADIST
• All Functions

References

Beta Distribution

• List of Main Z Functions

• Z3 home