Manuals/calci/BETADIST

BETADIST(x,alpha,beta,a,b)

• $x$ is the value between $a$ and $b$
• alpha and beta are the value of the shape parameter
• $a$ & $b$ the lower and upper limit to the interval of $x$.

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 $BETADIST(x,\alpha ,\beta ,a,b)$, $x$ is the value between $a$ and $b$.
• alpha is the value of the shape parameter.
• beta is the value of the shape parameter
• $a$ and $b$(optional) are the Lower and Upper limit to the interval of $x$.
• Normally $x$ lies between the limit $a$ and $b$, suppose when we are omitting $a$ and $b$ value, by default $x$ value with in 0 and 1.
• 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 $\beta \leq 0$
3.$x<a$ ,$x>b$, or $a=b$

• we are not mentioning the limit values $a$ and $b$,
• By default it will consider the Standard Cumulative Beta Distribution, a = 0 and b = 1.

Failed to parse (syntax error): {\displaystyle t^{\alpha−1} } Failed to parse (syntax error): {\displaystyle {x^{\alpha-1}} $f(x)={\frac {t^{\alpha -1}(1-t)^{\beta -1}dt}{B(\alpha ,\beta )}},$

ZOS

• The syntax is to calculate BEATDIST in ZOS is $BETADIST(Number,Alpha,Beta,LowerBound,UpperBound)$.
  • $Number$ is the value between LowerBound and UpperBound
  • $alpha$ and $beta$ are the value of the shape parameter.
• For e.g.,BETADIST(11..13,3,5,8,14)
• BETADIST(33..35,5..6,10..11,30,40)

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

Related Videos

Beta Distribution

See Also

• BETAINV
• All Functions

References

Beta Distribution

• List of Main Z Functions

• Z3 home