Difference between revisions of "Manuals/calci/BETADISTX"
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| − | ==beta | + | <div style="font-size:30px">'''BETADISTX(x,alpha,beta)'''</div><br/> |
| + | *<math>x</math> is the value between <math>a</math> and <math>b</math> | ||
| + | *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 <math>\alpha</math> and <math>\beta</math>. | ||
| + | *The Beta Distribution is also known as the Beta Distribution of the first kind. | ||
| + | *In <math>BETADIST(x,\alpha,\beta)</math>, <math>x</math> 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: | ||
| + | <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 : | ||
| + | <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. | ||
| + | *This function will give the result as error when | ||
| + | 1.Any one of the arguments are non-numeric. | ||
| + | 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> | ||
| + | *we are not mentioning the limit values <math>a</math> and <math>b</math>, | ||
| + | *By default it will consider the Standard Cumulative Beta Distribution, a = 0 and b = 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. | ||
| + | *For e.g.,BETADIST(11..13,3,5,8,14) | ||
| + | *BETADIST(33..35,5..6,10..11,30,40) | ||
| + | |||
| + | |||
| + | ==Examples== | ||
| + | #=BETADIST(0.4,8,10) = 0.35949234293309396 | ||
| + | #=BETADIST(3,5,9,2,6) = 0.20603810250759128 | ||
| + | #=BETADIST(9,4,2,8,11) = 0.04526748971193415 | ||
| + | #=BETADIST(5,-1,-2,4,7) = #ERROR | ||
| + | |||
| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|aZjUTx-E0Pk|280|center|Beta Distribution}} | ||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/BETAINV | BETAINV]] | ||
| + | *[[Manuals/calci/ALL | All Functions]] | ||
| + | |||
| + | ==References== | ||
| + | [http://en.wikipedia.org/wiki/Beta_distribution Beta Distribution] | ||
Revision as of 15:13, 7 December 2016
BETADISTX(x,alpha,beta)
- is the value between and
- alpha and beta are the value of the shape parameter
is the value between 
and 
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 :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)=\int_{0}^{x}\frac{t^{α−1}(1−t)^{\beta−1}dt} {B(\alpha,\beta)}} , 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 3. ,, or
or 
3.
,
, or 
- we are not mentioning the limit values and ,
- By default it will consider the Standard Cumulative Beta Distribution, a = 0 and b = 1.
ZOS
- The syntax is to calculate BEATDIST in ZOS is .
- is the value between LowerBound and UpperBound
- and 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)
.
is the value between LowerBound and UpperBound
and 
are the value of the shape parameter.
Examples
- =BETADIST(0.4,8,10) = 0.35949234293309396
- =BETADIST(3,5,9,2,6) = 0.20603810250759128
- =BETADIST(9,4,2,8,11) = 0.04526748971193415
- =BETADIST(5,-1,-2,4,7) = #ERROR