Size-Biased Sampling

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Abstract
Sampling components which are operating in a system at a fixed time and then observing the lifelengths of these components leads one to a length-biased sample. This concept is generalized to size-biased sampling, which often occurs when sampling multi-sized units such as particles. Estimators of average unit size are presented for the cases in which the underlying size distribution is gamma, Weibull or log-normal. These estimators, when specialized to the length-biased case, are shown to be improvements over some estimators already presented in the literature. Also, the problem of estimating mean life from backward recurrence times is discussed and some improved estimators are presented.

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