Difference between revisions of "Manuals/calci/BETADIST"

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<div style="font-size:30px">'''BETADIST(x,alpha,beta,a,b)'''</div><br/>
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<div style="font-size:30px">'''BETADIST (Number,Alpha,Beta,LowerBound,UpperBound)'''</div><br/>
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*x is the value between a and b,
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*<math>Number</math> is the value between <math>LowerBound</math> and <math>UpperBound</math>
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*alpha and beta are the value of the shape parameter
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*<math>Alpha</math> and <math>Beta</math> are the value of the shape parameter
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*a & b the lower and upper limit to the interval of x.
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*<math>LowerBound</math> & <math>UpperBound</math> the lower and upper limit to the interval of <math>Number</math>.
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**BETADIST(),returns the Beta Cumulative Distribution Function.
  
 
==Description==
 
==Description==
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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,a,b)</math>, <math>x</math> is the value between <math>a</math> and <math>b</math>.
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*In <math>(Number,Alpha,Beta,LowerBound,UpperBound)</math>, <math>Number</math> is the value between <math>LowerBound</math> and <math>UpperBound</math>.
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*alpha is the value of the shape parameter.
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*Alpha is the value of the shape parameter.
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*beta is the value of the shape parameter
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*Beta is the value of the shape parameter
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*<math>a</math> and <math>b</math>(optional) are  the Lower and Upper limit to the interval of <math>x</math>.
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*<math>LowerBound</math> and <math>UpperBound</math>(optional) are  the Lower and Upper limit to the interval of <math>Number</math>.
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*Normally <math>x</math> lies between the limit <math>a</math> and <math>b</math>, suppose when we are omitting  <math>a</math> and <math>b</math> value, by default <math>x</math> value with in 0 and 1.
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*Normally <math>Number</math> lies between the limit <math>LowerBound</math> and <math>UpperBound</math>, suppose when we are omitting  <math>LowerBound</math> and <math>UpperBound</math> value, by default <math>Number</math> value with in 0 and 1.
 
*The Probability Density Function of the beta distribution is:
 
*The Probability Density Function of the beta distribution is:
 
<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>0 ; <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  
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  1.Any one of the arguments are non-numeric
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  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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  3.<math>x<a</math> ,<math>x>b</math>, or a=b
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  3.<math>Number<LowerBound</math> ,<math>Number>UpperBound</math>, or <math>LowerBound=UpperBound</math>
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*we are not mentioning the limit values <math>a</math> and <math>b</math>,  
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*we are not mentioning the limit values <math>LowerBound</math> and <math>UpperBound</math>,  
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by default it will consider the Standard Cumulative Beta Distribution, a = 0 and b = 1.
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*By default it will consider the Standard Cumulative Beta Distribution, LowerBound = 0 and UpperBound = 1.
 +
 
 +
==ZOS==
 +
 
 +
*The syntax is to calculate BEATDIST in ZOS is <math>BETADIST (Number,Alpha,Beta,LowerBound,UpperBound)</math>.
 +
**<math>Number</math> is the value between LowerBound and UpperBound
 +
**<math>alpha</math> and <math>beta</math> are the value of the shape parameter.
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*For e.g.,BETADIST(11..13,3,5,8,14)
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*BETADIST(33..35,5..6,10..11,30,40)
 +
 
  
 
==Examples==
 
==Examples==
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#=BETADIST(0.4,8,10) = 0.359492343
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#=BETADIST(0.4,8,10) = 0.35949234293309396
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#=BETADIST(3,5,9,2,6) = 0.20603810250
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#=BETADIST(3,5,9,2,6) = 0.20603810250759128
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#=BETADIST(9,4,2,8,11) = 0.04526748971
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#=BETADIST(9,4,2,8,11) = 0.04526748971193415
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#=BETADIST(5,-1,-2,4,7) = NAN
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#=BETADIST(5,-1,-2,4,7) = #N/A (ALPHA GREATER THAN (OR) NOT EQUAL TO 0)
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 +
==Related Videos==
 +
 
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{{#ev:youtube|aZjUTx-E0Pk|280|center|Beta Distribution}}
  
 
==See Also==
 
==See Also==
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==References==
 
==References==
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[http://en.wikipedia.org/wiki/Beta_distribution Beta Distribution]
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[http://en.wikipedia.org/wiki/Beta_distribution Beta Distribution]
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 +
 
 +
 
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 03:57, 2 June 2020

BETADIST (Number,Alpha,Beta,LowerBound,UpperBound)


  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number} is the value between Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle LowerBound} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle UpperBound}
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Alpha} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Beta} are the value of the shape parameter
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle LowerBound} & Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle UpperBound} the lower and upper limit to the interval of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number} .
    • BETADIST(),returns the Beta Cumulative Distribution Function.

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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha} and .
  • The Beta Distribution is also known as the Beta Distribution of the first kind.
  • In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (Number,Alpha,Beta,LowerBound,UpperBound)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number} is the value between Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle LowerBound} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle UpperBound} .
  • Alpha is the value of the shape parameter.
  • Beta is the value of the shape parameter
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle LowerBound} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle UpperBound} (optional) are the Lower and Upper limit to the interval of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number} .
  • Normally Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number} lies between the limit Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle LowerBound} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle UpperBound} , suppose when we are omitting Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle LowerBound} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle UpperBound} value, by default Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number} value with in 0 and 1.
  • The Probability Density Function of the beta distribution is:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)=\frac{x^{\alpha-1}(1-x)^{ \beta-1}}{B(\alpha,\beta)},} where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 \le x \le 1} ; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha,\beta >0 } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B(\alpha,\beta)} 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 :

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F(x)=I_x(\alpha,\beta)} =Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_{0}^{x}f(x)=\frac{t^{\alpha-1}(1-t)^{ \beta-1}dt}{B(\alpha,\beta)}} , where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 \le t \le 1} ; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha,\beta>0} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B(\alpha,\beta)} is the Beta function.

  • This function will give the result as error when
1.Any one of the arguments are non-numeric.
2.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Alpha \le 0}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Beta \le 0}

3.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number<LowerBound}
 ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number>UpperBound}
, or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle LowerBound=UpperBound}
  • we are not mentioning the limit values Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle LowerBound} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle UpperBound} ,
  • By default it will consider the Standard Cumulative Beta Distribution, LowerBound = 0 and UpperBound = 1.

ZOS

  • The syntax is to calculate BEATDIST in ZOS is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle BETADIST (Number,Alpha,Beta,LowerBound,UpperBound)} .
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number} is the value between LowerBound and UpperBound
    • and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle beta} are the value of the shape parameter.
  • For e.g.,BETADIST(11..13,3,5,8,14)
  • BETADIST(33..35,5..6,10..11,30,40)


Examples

  1. =BETADIST(0.4,8,10) = 0.35949234293309396
  2. =BETADIST(3,5,9,2,6) = 0.20603810250759128
  3. =BETADIST(9,4,2,8,11) = 0.04526748971193415
  4. =BETADIST(5,-1,-2,4,7) = #N/A (ALPHA GREATER THAN (OR) NOT EQUAL TO 0)

Related Videos

Beta Distribution

See Also

References

Beta Distribution


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