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Not only in the field of Electrical Engineering,
but in the fields of Mechanical Engineering, Metal Engineering,
Pharmacology and Medical Science, the Weibull distribution is widely
used in discuss ing the probability distribution of breakdown, failure
and lifetime. Therefore, it is very important to estimate the Weibull
parameters and percentile points from the actual data. It has been
often used the Weibull probability chart to estimate the parameters
of the Weibull distribution. That is, the graphical method is taken.
This method has a good advantage that we can estimate the parameters
easily. On the contrary, there are some disadvantages such as the
inaccuracy in estimation and having no confidence. Thus, we have
to estimate the parameters with accuracy by the analytical methods
such as maximum likelihood estimation method, and then to calculate
the reliability of the estimates.
Here, I mainly describe the calculated results of reliability of
the estimates of the parameters and percentile points when all the
three parameters are unknown, along with the explanation of the
theoretical background. In addition, I describe the confidence limit
and confidence region with the method of asymptotic normal theory
of maximum likelihood estimation comparing with the method of likelihood
ratio test.
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