Difference between revisions of "Manuals/calci/WEIBULL"

Latest revision as of 16:32, 10 August 2018

WEIBULL (Number,Alpha,Beta,Cumulative)

$Number$ is the value of the function.
$Alpha$ and $Beta$ are the parameter of the distribution.
is the logical value.
- WEIBULL(),returns the Weibull distribution.

Description

This function gives the value of the weibull distribution with 2-parameters.
It is a continuous probability distribution.
Weibull distribution also called Rosin Rammler distribution.
It is used to model the lifetime of technical devices and is used to describe the particle size distribution of particles generated by grinding, milling and crushing operations.
This distribution is closely related to the lognormal distribution.
In $WEIBULL(Number,Alpha,Beta,Cumulative)$ , $Number$ is the value to evaluate the function.
$Alpha$ is the shape parameter of the distribution. $Beta$ is the scale parameter of the distribution.
$Cumulative$ is the logical value which determines the form of the distribution.
When $Cumulative$ is TRUE, this function gives the value of the cumulative distribution. When $Cumulative$ is FALSE, then this function gives the value of the probability density function.
When we are not omitting the value of $Cumulative$ , then it consider as FALSE.
Weibull distribution is of two type :3-parameter weibull distribution and 2-parameter weibull distribution.
This function gives the value of 2-parameter weibull distribution by setting the third parameter (location parameter) is zero.
Also if alpha<1,then the failure rate of the device decreases over time.
If alpha=1, then the failure rate of the device is constant over time.
If alpha>1, then the failure rate of the device increases over time.
The equation for cumulative distribution function is: $F(x,\alpha ,\beta )$ = $1-e^{-}{({\frac {x}{\beta }})}^{\alpha }$ .
The equation for probability density function is:

$f(x,\alpha ,\beta )={\frac {\alpha }{\beta ^{\alpha }}}.x^{\alpha -1}.e^{-}{({\frac {x}{\beta }})}^{\alpha }.$

When alpha =1, then this function gives the exponential with $\lambda ={\frac {1}{\beta }}$ .
This function gives the result as error when

   1. Any one of the argument is non-numeric.
   2. Number is negative.
   3. Alpha $\leq 0$  or Beta  $\leq 0$

Examples

=WEIBULL(202,60,81,TRUE) = 1
=WEIBULL(202,60,81,FALSE) = 0
=WEIBULL(160,80,170,TRUE) = 0.00779805060
=WEIBULL(160,80,170,FALSE) = 0.0038837823333
= WEIBULL(10.5,2.1,5.3,TRUE) = 0.9850433821261
=WEIBULL(10.5,2.1,5.3,FALSE) = 0.0125713406729

References

Weibull distribution

List of Main Z Functions

Z3 home

@@ Line 1: / Line 1: @@
-<div style="font-size:30px">'''WEIBULL(x,alpha,beta,lv)'''</div><br/>
+<div style="font-size:30px">'''WEIBULL (Number,Alpha,Beta,Cumulative) '''</div><br/>
-*<math>x </math>  is the value of the function.
+*<math>Number </math>  is the value of the function.
-*<math>alpha </math> and <math> beta </math> are the parameter of the distribution.
+*<math>Alpha </math> and <math> Beta </math> are the parameter of the distribution.
-*<math>lv</math> is the logical value.
+*<math>Cumulative</math> is the logical value.
+**WEIBULL(),returns the Weibull distribution.
 ==Description==
@@ Line 10: / Line 11: @@
 *It is used to model the lifetime of technical devices and is used to describe the particle size distribution of particles generated by grinding, milling and crushing operations.
 *This distribution is closely related to the lognormal distribution.
-*In <math>WEIBULL(x,alpha,beta,lv)</math>,<math> x </math> is the  value to evaluate the function.
+*In <math>WEIBULL(Number,Alpha,Beta,Cumulative)</math>,<math> Number </math> is the  value to evaluate the function.
-*<math> alpha </math> is the shape parameter of the distribution.<math> beta </math> is the scale parameter of the distribution.
+*<math> Alpha </math> is the shape parameter of the distribution.<math> Beta </math> is the scale parameter of the distribution.
-*<math>lv</math> is the logical value which determines the form of the distribution.
+*<math>Cumulative</math> is the logical value which determines the form of the distribution.
-*When <math>lv</math> is TRUE, this function gives the value of the cumulative distribution. When <math>lv</math> is FALSE, then this function gives the value of the probability density function.
+*When <math>Cumulative</math> is TRUE, this function gives the value of the cumulative distribution. When <math>Cumulative</math> is FALSE, then this function gives the value of the probability density function.
-*When we are not omitting the value of <math>lv</math>, then it consider as FALSE.
+*When we are not omitting the value of <math>Cumulative</math>, then it consider as FALSE.
 *Weibull distribution is of two type :3-parameter weibull distribution and 2-parameter weibull distribution.
 *This function gives the value of 2-parameter weibull distribution by setting the third parameter (location parameter) is zero.
@@ Line 20: / Line 21: @@
 *If alpha=1, then the failure rate of the device is constant over time.
 *If alpha>1, then the failure rate of the device increases over time.
-*The equation for cumulative distribution function is: <math>F(x,\alpha,\beta) = 1-e^-{(\frac{x}{β})}^α</math>
+*The equation for cumulative distribution function is: <math>F(x,\alpha,\beta)</math> =<math>1-e^-{(\frac{x}{\beta})}^\alpha</math>.
 *The equation for probability density function is:
 <math>f(x,\alpha,\beta) = \frac{\alpha}{\beta^\alpha}.x^{\alpha-1}.e^-{(\frac{x}{\beta})}^\alpha.</math>
@@ Line 26: / Line 27: @@
 *This function gives the result as error when
 . Any one of the argument is non-numeric.
-. x is negative.
+. Number is negative.
-. alpha<math>\le 0</math> or beta <math>\le 0</math>
+. Alpha<math>\le 0</math> or Beta <math>\le 0</math>
-<math>F(x,\alpha,\beta)</math> =<math>1-e^\frac{x}{\beta}^\alpha</math>
 ==Examples==
 #=WEIBULL(202,60,81,TRUE) = 1

Difference between revisions of "Manuals/calci/WEIBULL"

Latest revision as of 16:32, 10 August 2018

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