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 :

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 $0\leq x\leq 1$ 0 ; $\alpha ,\beta >0$ 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.