[distributions0]
Reliability Distributions


Birnbaum-Saunders
[top] [example]

The Birnbaum-Saunders distribution is defined by the pdf

   [distributions1][distributions2]

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

      [distributions3]
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

      [distributions4]

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

      [distributions5]

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

      [distributions6]
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

      [distributions7]

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

      [distributions8]

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

      [distributions9]
      
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

      [distributions10]

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

      [distributions11]

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

      [distributions12]

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

      [distributions13]

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

      [distributions14]

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

         [distributions15]

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

      [distributions16]

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

      [distributions17]

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

      [distributions18]

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

      [distributions19]

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

      [distributions20]

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)