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

1. BETADIST(0.4,8,10) = 0.359492343
2. BETADIST(3,5,9,2,6) = 0.20603810250
3. BETADIST(9,4,2,8,11) = 0.04526748971
4. BETADIST(5,-1,-2,4,7) = NAN

See Also

• Manuals/calci/BETAINV BETAINV

References

Beta Distribution