weibullness (version 1.24.1)

invweibull.mle: Maximum likelihood estimates of the two-parameter inverse Weibull distribution

Description

Calculates the maximum likelihood estimates of the two-parameter Weibull distribution.

Usage

invweibull.mle(x, interval, tol = .Machine$double.eps^0.25, maxiter = 1000, trace = 0)

Value

An object of class "weibull.estimate", a list with two parameter estimates.

Arguments

x

a numeric vector of observations.

interval

a vector containing the end-points of the interval to be estimated for the shape parameter.

tol

the desired accuracy (convergence tolerance).

maxiter

the maximum number of iterations.

trace

integer number; if positive, tracing information is produced. Higher values giving more details.

Author

Chanseok Park

Details

The two-parameter inverse Weibull distribution has the cumulative distribution function $$F(X)=\exp(-(\theta/x)^\beta)$$ where \(x>0\), \(\beta>0\) and \(\theta>0\).

The shape (\(\beta\)) and scale (\(\theta\)) parameters are estimated by calling weibull.mle on the reciprocally transformed data. The maximum likelihood estimation on the the reciprocally transformed data is performed using the method by Farnum and Booth (1997). If interval is missing, the interval is given by the method in Farnum and Booth (1997).

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).

References

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.

Examples

# 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)
invweibull.mle(data)