Difference between revisions of "Manuals/calci/BETADIST"
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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)=I_x(\alpha,\beta)=\int_{0}^{x}\frac{t^{α−1}(1−t)^{\beta−1}dt} {B( | + | <math>F(x)=I_x(\alpha,\beta)=\int_{0}^{x}\frac{t^{α−1}(1−t)^{\beta−1}dt} {B(\alpha,\beta)}</math>, where <math>0 \le x \le 1</math>0 ; <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 | ||
2.<math>\alpha \le 0</math> or <math>\beta \le 0</math> | 2.<math>\alpha \le 0</math> or <math>\beta \le 0</math> | ||
3.<math>x<a</math> ,<math>x>b</math>, or <math>a=b</math> | 3.<math>x<a</math> ,<math>x>b</math>, or <math>a=b</math> | ||
| − | + | *we are not mentioning the limit values <math>a</math> and <math>b</math>, | |
by default it will consider the Standard Cumulative Beta Distribution, <math>a = 0</math> and <math>b = 1</math>. | by default it will consider the Standard Cumulative Beta Distribution, <math>a = 0</math> and <math>b = 1</math>. | ||
Revision as of 23:36, 5 December 2013
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 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:
and 
.
, 
is the value between 
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_{0}^{x}\frac{t^{α−1}(1−t)^{\beta−1}dt} {B(\alpha,\beta)}} , where 0 ; 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, and .
or 
3.
,
, or 
*we are not mentioning the limit values 
and 
.
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