Reliability Distributions


Birnbaum-Saunders [top] [example]

The Birnbaum-Saunders distribution is defined by the pdf

   

where alpha and beta are shape parameters, Birnabaum and Saunders(1969). In the BUGS language it is used as

         x ~ dbs(alpha, beta)

Burr X [top] [example]

The Burr X distribution is defined by the pdf

      
where alpha is a shape parameter and lambda is a scale parameter, Surles and Padgett (2005) . In the Bugs language it is used as

         x ~ dburrX(alpha, lambda)
         
Burr XII [top] [example]

The Burr XII distribution is defined by the pdf

      

where alpha and beta are shape parameters, Klugman et al. (2004) . In the BUGS language it is used as

      x ~ dburrXII(alpha, beta)
         
Exponential Power [top] [example]

The Exponential power distribution is defined by the pdf

      

where alpha is a shape parameter and lambda a scale parameter, Smith and Bain (1975) . In the BUGS language it is used as

      x ~ dexp.power(alpha, lambda)
         
Exponentiated Weibull [top] [example]

The Exponentiated Weibul distribution is defined by the pdf

      
where alpha and theta are shape parameters, Mudholkar and Srivastava (1993) . In the BUGS language it is used as
         
         x ~ dexp.weib(alpha, theta)
         
Extended Exponential [top] [example]

The Extended Exponential distribution is defined by the pdf

      

where alpha is a shape parameter and lambda is a tilt parameter, Marshall and Olkin (1997, 2007) . In the BUGS language it is used as

         x ~ dext.exp(alpha, lambda)
         
Extended Weibull [top] [example]

The Extended Weibull distribution is dewfined by the pdf

      

where alpha is a shape parameter and lambda is a tilt parameter, Marshall and Olkin (1997, 2007) . In the BUGS language it is used as

         x ~ dext.weib(alpha, lambda)
         
Flexible Weibull [top] [example]

The Flexible Weibull distribution is dewfined by the pdf

      
      
where alpha and beta are shape parameters, Bebbington et al. (2007) . In the BUGS language it is used as

         x ~ dflex.weib(alpha, beta)
         

Generalized Exponential [top] [example]

The Generalized Exponential distribution is defined by the pdf

      

where alpha is a shape parameter and lambda is a scale parameter, Gupta and Kundu (1999, 2001) . In the BUGS language it is used as

      x ~ dgen.exp(alpha, lambda)
         
Generalized Power Webull [top] [example]

The Generalized Power Weibull distribution is defined by the pdf

      

where alpha and theta are shape parameters, Nikulin and Haghighi (2006) . In the BUGS language it is used as
      
      x ~ dgp.weib(alpha, theta)
                  
Gompertz [top] [example]

The Gompertz distribution is defined by the pdf

      

where alpha and theta are shape parameters, Marshall and Olkin (2007) . In the BUGS language it is used as

      x ~ dgpz(alpha, theta)
                  
Gumbel [top] [example]

The Gumbel distribution is defined by the pdf

      

where alpha is a location parameter and tau is a scale parameter, Marshall and Olkin (2007) . In the BUGS language it is used as

      x ~ dgumbel(alpha, tau)       
         
Inverse Gaussian [top] [example]

The Inverse Gaussian distribution is defined by the pdf

      

where mu is a location parameter and lambda is a scale parameter, Chhikara and Folks (1977) . In the BUGS language it is used as

      x ~ dinv.gauss(mu, lambda)
                  
Inverse Weibull [top] [example]

The Inverse Weibull distribution is defined by the pdf

         

where beta is a shape parameter and lambda is a scale parameter, Jiang and Murthy (2001) . In the BUGS language it is used as

      x ~ dinv.weib(beta, lambda)

Linear Failure Rate [top] [example]

The Linear Failure Rate distribution is defined by the pdf

      

where alpha and beta are shape parameters. Bain (1974) . In the BUGS language it is used as

      x ~ dlin.fr(alpha, beta)
         
Logistic Exponential [top] [example]

The Logistic Exponential distribution is defined by the pdf

      

where alpha is a shape parameter and lambda is a scale parameter, Lan and Leemis (2008) . In the BUGS language it is used as

      x ~ dlogistic.exp(alpha, lambda)

                  
Log-Logistic [top] [example]

The Log-Logistic distribution is defined by the pdf

      

where beta is a shape parameter and theta is a scale parameter, Lawless (2003) . In the BUGS language it is used as

      x ~ dlog.logis(beta, theta)    
      
Log-Weibull [top] [example]

The Log-Weibull distribution is defined by the pdf

      

where mu is a location parameter and sigma is a scale parameter, Murthy et al. (2004). In the BUGS language it is used as

      x ~ dlog.weib(mu, sigma)

Modified Weibull [top] [example]

The Modified Weibull distribution is defined by the pdf

      

where alpha and beta are shape parameters and lambda is a scale parameter, Lai et al..(2003) . In the BUGS language it is used as

      x ~ dweib.modified(alpha, beta, lambda)