Manuals/calci/BETADIST

BETADIST (Number,Alpha,Beta,LowerBound,UpperBound)

• $Number$ is the value between $LowerBound$ and $UpperBound$
• $Alpha$ and $Beta$ are the value of the shape parameter
• $LowerBound$ & $UpperBound$ the lower and upper limit to the interval of $Number$.
  • BETADIST(),returns the Beta Cumulative Distribution Function.

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 $(Number,Alpha,Beta,LowerBound,UpperBound)$, $Number$ is the value between $LowerBound$ and $UpperBound$.
• Alpha is the value of the shape parameter.
• Beta is the value of the shape parameter
• $LowerBound$ and $UpperBound$(optional) are the Lower and Upper limit to the interval of $Number$.
• Normally $Number$ lies between the limit $LowerBound$ and $UpperBound$, suppose when we are omitting $LowerBound$ and $UpperBound$ value, by default $Number$ 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.$Number<LowerBound$ ,$Number>UpperBound$, or $LowerBound=UpperBound$

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

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