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 $BETADIST(x,\alpha ,\beta )$, $x$ 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 :

Failed to parse (syntax error): {\displaystyle F(x)=I_x(\alpha,\beta)=\int_{0}^{x}\frac{t^{α−1}(1−t)^{\beta−1}dt} {B(\alpha,\beta)}} , where $0\leq x\leq 1$ ; $\alpha ,\beta >0$ 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. =BETADIST(0.4,8,10) = 0.35949234293309396
2. =BETADIST(3,5,9,2,6) = 0.20603810250759128
3. =BETADIST(9,4,2,8,11) = 0.04526748971193415
4. =BETADIST(5,-1,-2,4,7) = #ERROR

See Also

• BETADIST
• BETAINV
• All Functions

References

Beta Distribution