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)</math>=<math>\int_{0}^{x}f(x)=\frac{t^{\alpha-1}(1-t)^{ \beta-1}dt}{B(\alpha,\beta)}</math>, where <math>0 \le t \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 15:39, 22 January 2018
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 :=, where ; and is the Beta function.
=
, where 
; - This function will give the result as error when
1.Any one of the arguments are non-numeric. 2. or
or 
Examples
- =BETADISTX(0.67,9,12) = 0.3102416743686678
- =BETADISTX(6,34,37) = 2.576888446568541e+72
- =BETADISTX(100,456,467)= NaN
See Also
References