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In estimating the breakdown voltage, the Weibull
distribution is usually used. In this case, it often happens that
the location parameter y is strictly positive. This means that all
the 3 Weibull parameters are unknown. It is not easy to estimate
the unknown 3 parameters numerically by the ordinary maximum likelihood
estimation method(MLE). For instance, when O <b< 2, the maximum
likelihood estimates sometimes do not exist. Here, fl is the shape
parameter. Thus, a variety of parameter estimating methods were
proposed to avoid this difficulty. Percentile estimating methods(PE)
are one of these cases. Since MLE includes the numerical iterations,
there sometimes exists the case that parameters are diverging. On
the other hand if we use PE, we do not fail to get the estimates
and the calculation is quite simple. But in PE, the greater the
fl is, the greater the bias of the estimates are. In the case of
MLE, there exists the problem of divergence, i.e. in some cases,
the estimated parameters diverge. However, in the diverging process,
the likelihood seems to be converged. That is, at the large estimates,
the likelihoods are to be nearly equal, even if the estimates differ
to a great extent. Thus, I propose the new estimating procedure
of extended maximum likelihood estimation(EMLE). That is, the judgnlent
of the convergence in Newton-Raphson iteration procedure is taken
as the likelihood itself, but not the parameters. Using this idea,
we do not fail to estimate the low percentage point. Another advantage
concerning this method is the reduction of bias and mean square
error comparing with the closed form estimating methods such as
PE.
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