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, $\alpha$ ,Failed to parse (unknown function "\betab"): {\displaystyle \betab} ,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 $0/lex/le1$ ; $/alpha,/beta>0$ 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 $Ix$ and is defined as :

Failed to parse (syntax error): {\displaystyle F(x)=Ix(\alpha,\beta)=\int_{0}^{x}{t^{α−1}(1−t)^{\beta−1}dt} {B(p,q)}, where <math>0 \le x \le 1} 0 ; $\alpha ,\beta >0$ 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  $a=b$ 
4.we are not mentioning the limit values  $a$  and  $b$ , by default it will consider the standard cumulative beta distribution,  $a=0$  and  $b=1$ .