Difference between revisions of "Manuals/calci/BETADIST"

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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.
 
*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:
 
*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>Ix</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>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)}</math>,  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.
+
<math>F(x)=Ix(\alpha,\beta)=\int_{0}^{x}\frac{t^{α−1}(1−t)^{\beta−1}dt} {B(p,q)}</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.
 
*This function will give the result as error when  
 
*This function will give the result as error when  
 
  1.Any one of the arguments are non-numeric
 
  1.Any one of the arguments are non-numeric
 
  2.<math>\alpha \le 0</math> or <math>\beta \le 0</math>
 
  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>
 
  3.<math>x<a</math> ,<math>x>b</math>, or <math>a=b</math>
  4.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>.
+
  4.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==
 
==Examples==

Revision as of 05:39, 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 and .
  • The Beta Distribution is also known as the Beta Distribution of the first kind.
  • In , is the value between and .
  • alpha is the value of the shape parameter.
  • beta is the value of the shape parameter
  • and (optional) are the Lower and Upper limit to the interval of .
  • Normally lies between the limit and , suppose when we are omitting and value, by default value with in 0 and 1.
  • The Probability Density Function of the beta distribution is:

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 :

Failed to parse (syntax error): {\displaystyle F(x)=Ix(\alpha,\beta)=\int_{0}^{x}\frac{t^{α−1}(1−t)^{\beta−1}dt} {B(p,q)}} , where 0 ; 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 
4.we are not mentioning the limit values  and , 
by default it will consider the Standard Cumulative Beta Distribution,  and .

Examples

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

See Also


References

Beta Distribution