Difference between revisions of "Manuals/calci/BETADIST"

Latest revision as of 03:57, 2 June 2020

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

$Number$ is the value between $LowerBound$ and $UpperBound$
$Alpha$ and $Beta$ are the value of the shape parameter
& the lower and upper limit to the interval of .
- 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 $\alpha$ and $\beta$ .
The Beta Distribution is also known as the Beta Distribution of the first kind.
In $(Number,Alpha,Beta,LowerBound,UpperBound)$ , $Number$ is the value between $LowerBound$ and $UpperBound$ .
Alpha is the value of the shape parameter.
Beta is the value of the shape parameter
$LowerBound$ and $UpperBound$ (optional) are the Lower and Upper limit to the interval of $Number$ .
Normally $Number$ lies between the limit $LowerBound$ and $UpperBound$ , suppose when we are omitting $LowerBound$ and $UpperBound$ value, by default $Number$ value with in 0 and 1.
The Probability Density Function of the beta distribution is:

$f(x)={\frac {x^{\alpha -1}(1-x)^{\beta -1}}{B(\alpha ,\beta )}},$ where $0\leq x\leq 1$ ; $\alpha ,\beta >0$ and $B(\alpha ,\beta )$ is the Beta function.

The formula for the Cumulative Beta Distribution is called the Incomplete Beta function ratio and it is denoted by $I_{x}$ and is defined as :

$F(x)=I_{x}(\alpha ,\beta )$ = $\int _{0}^{x}f(x)={\frac {t^{\alpha -1}(1-t)^{\beta -1}dt}{B(\alpha ,\beta )}}$ , where $0\leq t\leq 1$ ; $\alpha ,\beta >0$ and $B(\alpha ,\beta )$ is the Beta function.

This function will give the result as error when

1.Any one of the arguments are non-numeric.
2. $Alpha\leq 0$  or  $Beta\leq 0$ 
3. $Number<LowerBound$  , $Number>UpperBound$ , or  $LowerBound=UpperBound$

we are not mentioning the limit values $LowerBound$ and $UpperBound$ ,
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 .
- $Number$ is the value between LowerBound and UpperBound
- $alpha$ and $beta$ 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

=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) = #N/A (ALPHA GREATER THAN (OR) NOT EQUAL TO 0)

References

Beta Distribution

List of Main Z Functions

Z3 home

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-<div style="font-size:30px">'''BETADIST(x,alpha,beta,a,b)'''</div><br/>
+<div style="font-size:30px">'''BETADIST (Number,Alpha,Beta,LowerBound,UpperBound)'''</div><br/>
-*x is the value between a and b,
+*<math>Number</math> is the value between <math>LowerBound</math> and <math>UpperBound</math>
-*alpha and beta are the value of the shape parameter
+*<math>Alpha</math> and <math>Beta</math> are the value of the shape parameter
-*a & b the lower and upper limit to the interval of x.
+*<math>LowerBound</math> & <math>UpperBound</math> the lower and upper limit to the interval of <math>Number</math>.
+**BETADIST(),returns the Beta Cumulative Distribution Function.
 ==Description==
-*This function gives the cumulative beta probability density function.
+*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 α and ß.
+*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 BETADIST(x,alpha,beta,a,b) x is the value between a and b, alpha is the value of the shape parameter,beta is the value of the shape parameter and a and b(optional) are  the lower and upper limit to the interval of x.
+*In <math>(Number,Alpha,Beta,LowerBound,UpperBound)</math>, <math>Number</math> is the value between <math>LowerBound</math> and <math>UpperBound</math>.
-*Normally x is lies between the limit a and b, suppose when we are omitting  the a and b value by default x value with in 0 and 1.
+*Alpha is the value of the shape parameter.
-*The probability density function of the beta distribution is:f(x)=x^ α-1(1-x)^ ß-1/B(α,ß), where 0≤x≤1; α,ß >0 and B(α,ß) is the Beta function.
+*Beta is the value of the shape parameter
-*The formula for the cumulative  beta distribution is  called the incomplete beta function ratio and it is denoted by Ix and is defined as
+*<math>LowerBound</math> and <math>UpperBound</math>(optional) are  the Lower and Upper limit to the interval of <math>Number</math>.
-F(x)=Ix(α,ß)=∫ limit 0 to x t^α−1(1−t)ß−1dt  /B(p,q),  where 0≤x≤1; α,ß>0 and B(α,ß) is the Beta function.
+*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:
+<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)</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
-. Any one of the arguments are non-numeric
+.Any one of the arguments are non-numeric.
-.alpha or beta<=0
+.<math>Alpha \le 0</math> or <math>Beta \le 0</math>
-.x<a ,x>b, or a=b
+.<math>Number<LowerBound</math> ,<math>Number>UpperBound</math>, or <math>LowerBound=UpperBound</math>
-. we are not mentioning the limit values a and b, by default it will consider the standard cumulative beta distribution, a= 0 and b= 1.
+*we are not mentioning the limit values <math>LowerBound</math> and <math>UpperBound</math>,
+*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.
+*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) = 0.359492343(Excel)
+#=BETADIST(0.4,8,10) = 0.35949234293309396
-                                  =NAN(calci)
+#=BETADIST(3,5,9,2,6) = 0.20603810250759128
-BETADIST(3,5,9,2,6) = 0.20603810250
+#=BETADIST(9,4,2,8,11) = 0.04526748971193415
-BETADIST(9,4,2,8,11) = 0.04526748971
+#=BETADIST(5,-1,-2,4,7) = #N/A (ALPHA GREATER THAN (OR) NOT EQUAL TO 0)
-BETADIST(5,-1,-2,4,7) = NAN
+==Related Videos==
+{{#ev:youtube|aZjUTx-E0Pk|280|center|Beta Distribution}}
 ==See Also==
-*[[Manuals/calci/BETAINV  BETAINV]]
+*[[Manuals/calci/BETAINV | BETAINV]]
+*[[Manuals/calci/ALL | All Functions]]
+==References==
+[http://en.wikipedia.org/wiki/Beta_distribution  Beta Distribution]
-==References==
-[http://en.wikipedia.org/wiki/Beta_distribution Beta Distribution]
+*[[Z_API_Functions | List of Main Z Functions]]
+*[[ Z3 |   Z3 home ]]

Difference between revisions of "Manuals/calci/BETADIST"

Latest revision as of 03:57, 2 June 2020

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