In a record breaking data set, only observations that above or below the normal values are recorded. Examples of this include extreme weather conditions, water levels in dams etc. Analysis of such data has many applications in the fields of insurance, stress testing, meteorological analysis and so on. The logarithm of a Weibull random variable follows the extreme value distribution. The estimation of parameters for such a distribution is also available. It is advisable to deal with Weibull distribution directly since transformed variables may not generate unbiased estimators. To overcome the drawbacks of the present estimation approaches, a new methodology is presented here, to obtain the shape parameter based on pivotal quantity and this can be used to reduce the bias of the scale parameter estimator. Exact confidence intervals for shape parameter and Weibull quantiles can be constructed based on the pivotal quantity. The confidence intervals for the mean and the reliability can be constructed based on generalized pivotal quantities that is a function of observed data and some random variables whose distributions are independent of unknown parameters. The inferences can be extended to stress-strength model. (39 refs.)
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