Difference between revisions of "Manuals/calci/BETADISTX"
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<math>f(x)=\frac{x^{\alpha-1}(1-x)^{ \beta-1}}{B(\alpha,\beta)},</math> where <math>0 \le x \le 1</math>; <math>\alpha,\beta >0 </math> and <math>B(\alpha,\beta)</math> is the Beta function. | <math>f(x)=\frac{x^{\alpha-1}(1-x)^{ \beta-1}}{B(\alpha,\beta)},</math> where <math>0 \le x \le 1</math>; <math>\alpha,\beta >0 </math> and <math>B(\alpha,\beta)</math> is the Beta function. | ||
*The formula for the Cumulative Beta Distribution is called the Incomplete Beta function ratio and it is denoted by <math>I_x</math> and is defined as : | *The formula for the Cumulative Beta Distribution is called the Incomplete Beta function ratio and it is denoted by <math>I_x</math> and is defined as : | ||
| − | <math>F(x)= | + | <math>F(x)=I_{x}(\alpha,\beta)=\int\limits_{0}^{x}\frac{t^{α−1}(1−t)^{\beta−1}dt} {B(\alpha,\beta)}</math>, where <math>0 \le x \le 1</math> ; <math>\alpha,\beta>0</math> and <math>B(\alpha,\beta)</math> is the Beta function. |
*This function will give the result as error when | *This function will give the result as error when | ||
1.Any one of the arguments are non-numeric. | 1.Any one of the arguments are non-numeric. | ||
Revision as of 14:24, 7 December 2016
BETADISTX(x,alpha,beta)
- is any real number.
- alpha and beta are the value of the shape parameter
is any real number.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 any real number.
- alpha is the value of the shape parameter.
- beta is the value of the shape parameter
- The Probability Density Function of the beta distribution is:
and 
.
, where ; and is the Beta function.
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 :
and is defined as :Failed to parse (syntax error): {\displaystyle F(x)=I_{x}(\alpha,\beta)=\int\limits_{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
or 
Examples
- =BETADIST(0.4,8,10) = 0.35949234293309396
- =BETADIST(3,5,9,2,6) = 0.20603810250759128
- =BETADIST(9,4,2,8,11) = 0.04526748971193415
- =BETADIST(5,-1,-2,4,7) = #ERROR