Manuals/calci/BETADISTX

BETADISTX(x,alpha,beta)

• $x$ is any real number.
• alpha and beta are the value of the shape parameter

Description

• This function gives the Cumulative Beta Probability Density function.
• The beta distribution is a family of Continuous Probability Distributions defined on the interval [0, 1] parameterized by two positive shape parameters, denoted by $\alpha$ and $\beta$.
• The Beta Distribution is also known as the Beta Distribution of the first kind.
• In $BETADISTX(x,\alpha ,\beta )$, $x$ is any real number.
• alpha is the value of the shape parameter.
• beta is the value of the shape parameter
• The Probability Density Function of the beta distribution is:

$f(x)={\frac {x^{\alpha -1}(1-x)^{\beta -1}}{B(\alpha ,\beta )}},$ where $0\leq x\leq 1$; $\alpha ,\beta >0$ and $B(\alpha ,\beta )$ is the Beta function.

• The formula for the Cumulative Beta Distribution is called the Incomplete Beta function ratio and it is denoted by $I_{x}$ and is defined as :

$F(x)=I_{x}(\alpha ,\beta )$=$\int _{0}^{x}f(x)={\frac {t^{\alpha -1}(1-t)^{\beta -1}dt}{B(\alpha ,\beta )}}$, where $0\leq t\leq 1$ ; $\alpha ,\beta >0$ and $B(\alpha ,\beta )$ is the Beta function.

• This function will give the result as error when

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

Examples

1. =BETADISTX(0.67,9,12) = 0.3102416743686678
2. =BETADISTX(6,34,37) = 2.576888446568541e+72
3. =BETADISTX(100,456,467)= NaN

See Also

• BETADIST
• BETAINV
• All Functions

References

Beta Distribution

• List of Main Z Functions

• Z3 home