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.
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*In <math>BETADIST(x,\alpha,\beta)</math>, <math>x</math> is any real number.
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*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 :
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<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> ; <math>\alpha,\beta>0</math> and <math>B(\alpha,\beta)</math> is the Beta function.
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<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.
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  2.<math>\alpha \le 0</math> or <math>\beta \le 0</math>
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  2.<math>alpha \le 0</math> or <math>beta \le 0</math>
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==Examples==
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#=BETADISTX(0.67,9,12) = 0.3102416743686678
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#=BETADISTX(6,34,37) = 2.576888446568541e+72
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#=BETADISTX(100,456,467)= NaN
  
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==Examples==
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==Related Videos==
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#=BETADIST(0.4,8,10) = 0.35949234293309396
 
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#=BETADIST(3,5,9,2,6) = 0.20603810250759128
 
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#=BETADIST(9,4,2,8,11) = 0.04526748971193415
 
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#=BETADIST(5,-1,-2,4,7) = #ERROR
 
  
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{{#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]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 15:01, 4 December 2018

BETADISTX(x,alpha,beta)


  • is any real number.
  • alpha and beta are the value of the shape parameter

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:

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 :

=, 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

Examples

  1. =BETADISTX(0.67,9,12) = 0.3102416743686678
  2. =BETADISTX(6,34,37) = 2.576888446568541e+72
  3. =BETADISTX(100,456,467)= NaN

Related Videos

Beta Distribution

See Also

References

Beta Distribution


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