Calculates the maximum likelihood estimates of three-parameter Weibull distribution.
weibull.mle(x, threshold, interval, interval.threshold, extendInt="downX",
a, tol = .Machine$double.eps^0.25, maxiter = 1000, trace = 0)An object of class "weibull.estimate", a list with
two parameter estimates (if threshold is given) or three parameter estimates.
a numeric vector of observations.
the threshold parameter value.
a vector containing the end-points of the interval to be estimated for the shape parameter.
a vector containing the end-points of the interval to be estimated for the threshold parameter.
character string specifying if the interval c(left,right) should be extended or directly produce an error when f() has no differing signs at the endpoints. The default, "downX", keep lowering the the left end of the interval so that f() has different signs. See uniroot.
the offset fraction to be used; typically in (0,1).
the desired accuracy (convergence tolerance).
the maximum number of iterations.
integer number; if positive, tracing information is produced. Higher values giving more details.
Chanseok Park
The three-parameter Weibull distribution has the cumulative distribution function
$$F(x) = 1 - \exp\Big[ - \Big( \frac{x-\theta}{\beta} \Big)^{\alpha} \Big],$$
where \(x>\theta\).
The shape (\(\alpha\)) and scale (\(\beta\)) parameters are estimated
using the maximum likelihood.
The maximum likelihood estimation is performed using the method by
Farnum and Booth (1997).
If the threshold (\(\theta\)) is missing, it is estimated by
weibull.threshold.
If threshold=0, then weibull.mle calculates the maximum likelihood
estimates of the two-parameter Weibull distribution.
If interval is missing, the interval is given by the method in
Farnum and Booth (1997).
If interval.threshold is missing, the interval is initally given
by (min(x)-sd(x), min(x)). If this interval does not include
the estimate, its lower bound is extended (see also uniroot).
The choice of a follows ppoints function.
Convergence is declared either if f(x) == 0
or the change in x for one step of the algorithm is less than
tol (see also uniroot).
If the algorithm does not converge in maxiter steps,
a warning is printed and the current approximation is returned
(see also uniroot).
Park, C. (2018).
A Note on the Existence of the Location Parameter Estimate of the Three-Parameter Weibull Model Using the Weibull Plot.
Mathematical Problems in Engineering,
2018, 1-6.
https://doi.org/10.1155/2018/6056975
Park, C. (2017).
Weibullness test and parameter estimation of the three-parameter
Weibull model using the sample correlation coefficient.
International Journal of Industrial Engineering - Theory,
Applications and Practice,
24(4), 376-391.
http://journals.sfu.ca/ijietap/index.php/ijie/article/view/2848
Farnum, N. R. and P. Booth (1997). Uniqueness of Maximum Likelihood Estimators of the 2-Parameter Weibull Distribution. IEEE Transactions on Reliability, 46, 523-525.
library(weibullness)
# Three-parameter Weibull
data = c(355,725,884,462,1092,190,166,172,188,224,267,298,355,471,
154,101,76,811,80,249,752,305,301,386,667,212,186,127,
121,214,242,237,355,210,253,400,401,514,211,285)
weibull.mle(data)
# Two-parameter Weibull
weibull.mle(data, threshold=0)
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