Manuals/calci/CHIINV

CHIINV(probability,degreesoffreedom)

• Where $probability$ is the value associated with the Chi-squared Distribution
• $degreesoffreedom$ is the number of Degrees of Freedom

Description

• This function gives the inverse value of One_tailed probability of the Chi-squared Distribution.
• It is called Inverted-Chi-square Distribution and it is a Continuous Probability Distribution of a positive-valued random variable.

• Degrees of freedom $df$=$(r-1)(c-1)$.
• The $\chi ^{2}$ static used to compare the observed value in each table to the value which would be the expected under the assumption.
• If $X$ has the chi-squared distribution with n degrees of freedom, then according to the definition, ${\frac {1}{X}}$ has the Inverse-chi-squared distribution with $n$ degrees of freedom;
• If $CHIDIST(x,df)=prob$, then $CHIINV(prob,df)=x$.
• CHIINV 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.$df$ value is not an integer
3.$df<1$or $df>10^{10}$
4.Also $prob<0$ or $prob>1$.

ZOS Section

• The syntax is to calculate CHIINV in ZOS is $CHIINV(probability,degreesoffreedom)$.
  • Where $probability$ is the value associated with the Chi-squared Distribution
  • $degreesoffreedom$ is the number of Degrees of Freedom
• For e.g.,CHIINV(0.0257,3)

Inverse Chi-Squared Distribution

Examples

1. CHIINV(0.0001234098,2) = 18
2. CHIINV(0.2547876,5) = 6.5669999999999655
3. CHIINV(0.157299207050,1) = 1.9991000000000005
4. CHIINV(0.6785412,-1) = NAN

See Also

• CHIDIST
• CHITEST

References

Inverse-chi-squared Distribution