Difference between revisions of "Manuals/calci/BETADIST"

Revision as of 05:06, 3 December 2013

BETADIST(x,alpha,beta,a,b)

x is the value between a and b,
alpha and beta are the value of the shape parameter
a & b 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 BETADIST(x, $\alpha$ ,Failed to parse (unknown function "\betab"): {\displaystyle \betab} ,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
$a$ and $b$ (optional) are the Lower and Upper limit to the interval of $x$ .
Normally $x$ lies between the limit $a$ and $b$ , 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 $0/lex/le1$ ; $/alpha,/beta>0$ 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 $Ix$ 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)=Ix(\alpha,\beta)=\int_{0}^{x}{t^{α−1}(1−t)^{\beta−1}dt} {B(p,q)}, where <math>0 \le x \le 1} 0 ; $\alpha ,\beta >0$ 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. $x<a$  , $x>b$ , or  $a=b$ 
4.we are not mentioning the limit values  $a$  and  $b$ , by default it will consider the standard cumulative beta distribution,  $a=0$  and  $b=1$ .

Examples

BETADIST(0.4,8,10) = 0.359492343
BETADIST(3,5,9,2,6) = 0.20603810250
BETADIST(9,4,2,8,11) = 0.04526748971
BETADIST(5,-1,-2,4,7) = NAN

References

Beta Distribution

@@ Line 5: / Line 5: @@
 ==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 BETADIST(x,<math>\alpha</math>,<math>\betab</math>,a,b) <math>x</math> is the value between <math>a</math> and <math>b</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>a</math> and <math>b</math>(optional) are  the Lower and Upper limit to the interval of <math>x</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>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.
+*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>Ix</math> and is defined as :
+<math>F(x)=Ix(\alpha,\beta)=\int_{0}^{x}{t^{α−1}(1−t)^{\beta−1}dt} {B(p,q)},  where <math>0 \le x \le 1</math>0 ; <math>\alpha,\beta>0</math>0 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>x<a</math> ,<math>x>b</math>, or <math>a=b</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>a</math> and <math>b</math>, by default it will consider the standard cumulative beta distribution, <math>a = 0</math> and <math>b = 1</math>.
 ==Examples==

Difference between revisions of "Manuals/calci/BETADIST"

Revision as of 05:06, 3 December 2013

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Description

Examples

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