Changes

*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.  

*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.  

*This distribution is closely related to the lognormal distribution.  

*In WEIBULL(x,alpha,beta,lv),x is the  value to evaluate the function.

*In <math>WEIBULL(x,alpha,beta,lv)</math>,<math> x </math> is the  value to evaluate the function.

*alpha is the shape parameter of the distribution.beta 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.

*lv is the logical value which determines the form of the distribution.  

*<math>lv</math> is the logical value which determines the form of the distribution.  

*When lv is TRUE, this function gives the value of the cumulative distribution. When lv is FALSE, then this function gives the value of the probability density function.  

*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 we are not omitting the value of lv, then it consider as FALSE.  

*When we are not omitting the value of <math>lv</math>, then it consider as FALSE.  

*Weibull distribution is of two type :3-parameter weibull distribution and 2-parameter weibull distribution.  

*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.

*This function gives the value of 2-parameter weibull distribution by setting the third parameter (location parameter) is zero.

*If alpha=1, then the failure rate of the device is constant 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.  

*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}{\beta})}^\alpha</math>.

*The equation for cumulative distribution function is: <math>F(x,\alpha,\beta) = 1-e^-{(\frac{x}{β})}^α</math>

*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 exponentail with λ=1/β.

*When alpha =1, then this function gives the exponentail 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.