Difference between revisions of "Manuals/calci/WEIBULL"
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*<math>x </math> is the value of the function. | *<math>x </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>lv</math> is the logical value. |
==Description== | ==Description== | ||
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*The equation for probability density function is: | *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> | <math>f(x,\alpha,\beta) = \frac{\alpha}{\beta^\alpha}.x^{\alpha-1}.e^-{(\frac{x}{\beta})}^\alpha.</math> | ||
| − | *When alpha =1, then this function gives the | + | *When alpha =1, then this function gives the exponential with <math>\lambda=\frac{1}{\beta}</math>. |
*This function gives the result as error when | *This function gives the result as error when | ||
1. Any one of the argument is non-numeric. | 1. Any one of the argument is non-numeric. | ||
2. x is negative. | 2. x is negative. | ||
| − | 3.alpha<math>\le 0</math> or beta <math>\le 0. | + | 3. alpha<math>\le 0</math> or beta <math>\le 0. |
| − | WEIBULL( | + | ==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 | ||
| − | + | ==See Also== | |
| + | *[[Manuals/calci/EXPONDIST | EXPONDIST ]] | ||
| + | *[[Manuals/calci/LOGNORM | LOGNORM ]] | ||
| − | + | ==References== | |
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Revision as of 22:25, 9 February 2014
WEIBULL(x,alpha,beta,lv)
- is the value of the function.
- and are the parameter of the distribution.
- is the logical value.
is the value of the function.
and 
are the parameter of the distribution.
is the logical value.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 , is the value to evaluate the function.
- is the shape parameter of the distribution. is the scale parameter of the distribution.
- is the logical value which determines the form of the distribution.
- When is TRUE, this function gives the value of the cumulative distribution. When is FALSE, then this function gives the value of the probability density function.
- When we are not omitting the value of , 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: Failed to parse (syntax error): {\displaystyle F(x,\alpha,\beta) = 1-e^-{(\frac{x}{β})}^α}
- The equation for probability density function is:
,
- When alpha =1, then this function gives the exponential with .
- This function gives the result as error when
.1. Any one of the argument is non-numeric. 2. x is negative. 3. alpha or beta <math>\le 0.
or beta <math>\le 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