Difference between revisions of "Manuals/calci/BETADIST"

Revision as of 15:17, 19 January 2018

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 :

$F(x)=I_{x}(\alpha ,\beta )$ =Failed to parse (syntax error): {\displaystyle \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  $\beta \leq 0$ 
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 (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {x^{\alpha-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)