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 $x$ .

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 $(Number,Alpha,Beta,LowerBound,UpperBound)$ , $Number$ 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 $a$ 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. $Number<LowerBound$  , $Number>UpperBound$ , 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 .
- $Number$ 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)