Reliability Distributions
Birnbaum-Saunders
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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)