Difference between revisions of "Manuals/calci/BETADISTX"
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*The beta distribution is a family of Continuous Probability Distributions defined on the interval [0, 1] parameterized by two positive shape parameters, denoted by <math>\alpha</math> and <math>\beta</math>. | *The beta distribution is a family of Continuous Probability Distributions defined on the interval [0, 1] parameterized by two positive shape parameters, denoted by <math>\alpha</math> and <math>\beta</math>. | ||
*The Beta Distribution is also known as the Beta Distribution of the first kind. | *The Beta Distribution is also known as the Beta Distribution of the first kind. | ||
| − | *In <math>BETADISTX(x, | + | *In <math>BETADISTX(x,alpha,beta)</math>, <math>x</math> is any real number. |
*alpha is the value of the shape parameter. | *alpha is the value of the shape parameter. | ||
*beta is the value of the shape parameter | *beta is the value of the shape parameter | ||
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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. | ||
| − | 2.<math> | + | 2.<math>alpha \le 0</math> or <math>beta \le 0</math> |
==Examples== | ==Examples== | ||
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#=BETADISTX(6,34,37) = 2.576888446568541e+72 | #=BETADISTX(6,34,37) = 2.576888446568541e+72 | ||
#=BETADISTX(100,456,467)= NaN | #=BETADISTX(100,456,467)= NaN | ||
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| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|aZjUTx-E0Pk|280|center|Beta Distribution}} | ||
==See Also== | ==See Also== | ||
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==References== | ==References== | ||
[http://en.wikipedia.org/wiki/Beta_distribution Beta Distribution] | [http://en.wikipedia.org/wiki/Beta_distribution Beta Distribution] | ||
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| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | |||
| + | *[[ Z3 | Z3 home ]] | ||
Latest revision as of 16:01, 4 December 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
Related Videos
See Also
References