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 α and ß.
- 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 and a and b(optional) are the lower and upper limit to the interval of x.
- Normally x is lies between the limit a and b, suppose when we are omitting the a and b value by default x value with in 0 and 1.
- The probability density function of the beta distribution is:f(x)=x^ α-1(1-x)^ ß-1/B(α,ß), where 0≤x≤1; α,ß >0 and B(α,ß) 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
F(x)=Ix(α,ß)=∫ limit 0 to x t^α−1(1−t)ß−1dt /B(p,q), where 0≤x≤1; α,ß>0 and B(α,ß) is the Beta function.
- This function will give the result as error when
1. Any one of the arguments are non-numeric 2.alpha or beta<=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.
Examples
- BETADIST(0.4,8,10) = 0.359492343
- BETADIST(3,5,9,2,6) = 0.20603810250
- BETADIST(9,4,2,8,11) = 0.04526748971
- BETADIST(5,-1,-2,4,7) = NAN
See Also