Manuals/calci/BETADIST

BETADIST(x,alpha,beta,a,b)


  • is the value between and
  • alpha and beta are the value of the shape parameter
  • & the lower and upper limit to the interval of .

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   and  .
  • The Beta Distribution is also known as the Beta Distribution of the first kind.
  • In  ,   is the value between   and  .
  • alpha is the value of the shape parameter.
  • beta is the value of the shape parameter
  •   and  (optional) are the Lower and Upper limit to the interval of  .
  • Normally   lies between the limit   and  , suppose when we are omitting   and   value, by default   value with in 0 and 1.
  • The Probability Density Function of the beta distribution is:

  where  ;   and   is the Beta function.

  • The formula for the Cumulative Beta Distribution is called the Incomplete Beta function ratio and it is denoted by   and is defined as :

 =Failed to parse (syntax error): {\displaystyle \int_{0}^{x}\frac{t^{α−1}(1−t)^{\beta−1}dt} {B(\alpha,\beta)}} , where   ;   and   is the Beta function.

  • This function will give the result as error when
1.Any one of the arguments are non-numeric.
2.  or  
3.  , , or  
  • we are not mentioning the limit values   and  ,
  • 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 (syntax error): {\displaystyle {x^{\alpha-1}}

ZOS

  • The syntax is to calculate BEATDIST in ZOS is  .
    •   is the value between LowerBound and UpperBound
    •   and   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)


Examples

  1. =BETADIST(0.4,8,10) = 0.35949234293309396
  2. =BETADIST(3,5,9,2,6) = 0.20603810250759128
  3. =BETADIST(9,4,2,8,11) = 0.04526748971193415
  4. =BETADIST(5,-1,-2,4,7) = #ERROR

Related Videos

Beta Distribution

See Also

References

Beta Distribution