Reliability distributions
Birnbaum-Saunders
The Birnbaum-Saunders distribution [example] is defined by the pdf![[distributions1]](distributions1.bmp)
![[distributions2]](distributions2.bmp)
where
alpha and beta are shape parameters, Birnabaum and Saunders (1969). In the BUGS language it is used asx ~ dbs(alpha, beta)Burr X
The Burr X distribution [example] is defined by the pdf
![[distributions3]](distributions3.bmp)
where
alpha is a shape parameter and lambda is a scale parameter, Surles and Padgett (2005). In the BUGS language it is used asx ~ dburrX(alpha, lambda)Burr XII
The Burr XII distribution [example] is defined by the pdf
![[distributions4]](distributions4.bmp)
where
alpha and beta are shape parameters, Klugman et al. (2004). In the BUGS language it is used asx ~ dburrXII(alpha, beta)Exponential Power
The Exponential power distribution [example] is defined by the pdf![[distributions5]](distributions5.bmp)
where
alpha is a shape parameter and lambda a scale parameter, Smith and Bain (1975). In the BUGS language it is used asx ~ dexp.power(alpha, lambda)Exponentiated Weibull
The Exponentiated Weibul distribution [example] is defined by the pdf![[distributions6]](distributions6.bmp)
where
alpha and theta are shape parameters, Mudholkar and Srivastava (1993). In the BUGS language it is used asx ~ dexp.weib(alpha, theta)Extended Exponential
The Extended Exponential distribution [example] is defined by the pdf![[distributions7]](distributions7.bmp)
where
alpha is a shape parameter and lambda is a tilt parameter, Marshall and Olkin (1997, 2007). In the BUGS language it is used asx ~ dext.exp(alpha, lambda)Extended Weibull
The Extended Weibull distribution [example] is defined by the pdf![[distributions8]](distributions8.bmp)
where
alpha is a shape parameter and lambda is a tilt parameter, Marshall and Olkin (1997, 2007). In the BUGS language it is used asx ~ dext.weib(alpha, lambda)Flexible Weibull
The Flexible Weibull distribution [example] is defined by the pdf![[distributions9]](distributions9.bmp)
where
alpha and beta are shape parameters, Bebbington et al. (2007). In the BUGS language it is used asx ~ dflex.weib(alpha, beta)Generalized Exponential
The Generalized Exponential distribution [example] is defined by the pdf![[distributions10]](distributions10.bmp)
where
alpha is a shape parameter and lambda is a scale parameter, Gupta and Kundu (1999, 2001). In the BUGS language it is used asx ~ dgen.exp(alpha, lambda)Generalized Power Weibull
The Generalized Power Weibull distribution [example] is defined by the pdf![[distributions11]](distributions11.bmp)
where
alpha and theta are shape parameters, Nikulin and Haghighi (2006). In the BUGS language it is used asx ~ dgp.weib(alpha, theta)Gompertz
The Gompertz distribution [example] is defined by the pdf![[distributions12]](distributions12.bmp)
where
alpha and theta are shape parameters, Marshall and Olkin (2007). In the BUGS language it is used asx ~ dgpz(alpha, theta)Gumbel
The Gumbel distribution [example] is defined by the pdf![[distributions13]](distributions13.bmp)
where
alpha is a location parameter and tau is a scale parameter, Marshall and Olkin (2007). In the BUGS language it is used asx ~ dgumbel(alpha, tau)Inverse Gaussian
The Inverse Gaussian distribution [example] is defined by the pdf![[distributions14]](distributions14.bmp)
where
mu is a location parameter and lambda is a scale parameter, Chhikara and Folks (1977). In the BUGS language it is used asx ~ dinv.gauss(mu, lambda)Inverse Weibull
The Inverse Weibull distribution [example] is defined by the pdf![[distributions15]](distributions15.bmp)
where
beta is a shape parameter and lambda is a scale parameter, Jiang and Murthy (2001). In the BUGS language it is used asx ~ dinv.weib(beta, lambda)Linear Failure Rate
The Linear Failure Rate distribution [example] is defined by the pdf![[distributions16]](distributions16.bmp)
where
alpha and beta are shape parameters. Bain (1974). In the BUGS language it is used asx ~ dlin.fr(alpha, beta)Logistic Exponential
The Logistic Exponential distribution [example] is defined by the pdf![[distributions17]](distributions17.bmp)
where
alpha is a shape parameter and lambda is a scale parameter, Lan and Leemis (2008). In the BUGS language it is used asx ~ dlogistic.exp(alpha, lambda)Log-logistic
The Log-Logistic distribution [example] is defined by the pdf![[distributions18]](distributions18.bmp)
where
beta is a shape parameter and theta is a scale parameter, Lawless (2003). In the BUGS language it is used asx ~ dlog.logis(beta, theta)Log-Weibull
The Log-Weibull distribution [example] is defined by the pdf![[distributions19]](distributions19.bmp)
where
mu is a location parameter and sigma is a scale parameter, Murthy et al. (2004). In the BUGS language it is used asx ~ dlog.weib(mu, sigma)Modified Weibull
The Modified Weibull distribution [example] is defined by the pdf![[distributions20]](distributions20.bmp)
where a
lpha and beta are shape parameters and lambda is a scale parameter, Lai et al..(2003). In the BUGS language it is used asx ~ dweib.modified(alpha, beta, lambda)