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

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)

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)

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)

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)

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)

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)

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)

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)

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)