Difference between revisions of "Manuals/calci/BETADIST"

Revision as of 16:14, 12 June 2018

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

$Number$ is the value between $LowerBound$ and $UpperBound$
$Alpha$ and $Beta$ are the value of the shape parameter
$LowerBound$ & $UpperBound$ the lower and upper limit to the interval of $x$ .

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 $a$ and $b$ value, by default $x$ 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) = #ERROR

References

Beta Distribution

List of Main Z Functions

Z3 home

@@ Line 1: / Line 1: @@
-<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/>
-*<math>x</math> is the value between <math>a</math> and <math>b</math>
+*<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
-*<math>a</math> & <math>b</math> the lower and upper limit to the interval of <math>x</math>.
+*<math>LowerBound</math> & <math>UpperBound</math> the lower and upper limit to the interval of <math>x</math>.
 ==Description==
@@ Line 8: / Line 8: @@
 *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,a,b)</math>, <math>x</math> is the value between <math>a</math> and <math>b</math>.
+*In <math>(Number,Alpha,Beta,LowerBound,UpperBound)</math>, <math>Number</math> is the value between <math>LowerBound</math> and <math>UpperBound</math>.
-*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
-*<math>a</math> and <math>b</math>(optional) are  the Lower and Upper limit to the interval of <math>x</math>.
+*<math>LowerBound</math> and <math>UpperBound</math>(optional) are  the Lower and Upper limit to the interval of <math>Number</math>.
-*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.
+*Normally <math>Number</math> lies between the limit <math>LowerBound</math> and <math>UpperBound</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.
 *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.
@@ Line 19: / Line 19: @@
 *This function will give the result as error when
 .Any one of the arguments are non-numeric.
-.<math>\alpha \le 0</math> or <math>\beta \le 0</math>
+.<math>Alpha \le 0</math> or <math>Beta \le 0</math>
-.<math>x<a</math> ,<math>x>b</math>, or <math>a=b</math>
+.<math>Number<LowerBound</math> ,<math>Number>UpperBound</math>, or <math>LowerBound=UpperBound</math>
-*we are not mentioning the limit values <math>a</math> and <math>b</math>,
+*we are not mentioning the limit values <math>LowerBound</math> and <math>UpperBound</math>,
-*By default it will consider the Standard Cumulative Beta Distribution, a = 0 and b = 1.
+*By default it will consider the Standard Cumulative Beta Distribution, LowerBound = 0 and UpperBound = 1.
 ==ZOS==

Difference between revisions of "Manuals/calci/BETADIST"

Revision as of 16:14, 12 June 2018

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