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Uniqueness of maximum likelihood estimators of the 2-parameter Weibull distribution

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2 Author(s)
Farnum, Nicholas R. ; Dept. of Manage. Sci. & Inf. Syst., California State Univ., Fullerton, CA, USA ; Booth, P.

We present a simple statistic, calculated from either complete failure data or from right-censored data of type-I or -II. It is useful for understanding the behavior of the parameter maximum likelihood estimates (MLE) of a 2-parameter Weibull distribution. The statistic is based on the logarithms of the failure data and can be interpreted as a measure of variation in the data. This statistic provides: (a) simple lower bounds on the parameter MLE, and (b) a quick approximation for parameter estimates that can serve as starting points for iterative MLE routines; it can be used to show that the MLE for the 2-parameter Weibull distribution are unique

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Reliability, IEEE Transactions on  (Volume:46 ,  Issue: 4 )