Record-breaking data: A parametric comparison of the inverse-sampling and the random-sampling schemes
In many industrial quality control experiments and destructive stress testing, the only available data are successive minima (or maxima), i.e., record-breaking data. There are two sampling schemes used to collect record-breaking data: random sampling and inverse sampling. For random sampling, the total sample size is predetermined and the number of records is a random variable while in inverse-sampling the number of records to be observed is predetermined; thus the sample size is a random variable. The purpose of this paper is to determine, via simulations, which of the two schemes, if any, is more efficient. Since the two schemes are equivalent asymptotically, the simulations were carried out for small to moderate sized record-breaking samples. Simulated biases and mean square errors of the maximum likelihood estimators of the parameters using the two sampling schemes were compared. In general, it was found I:hat if the estimators were well behaved, then there was no significant difference between the mean square errors of the estimates for the two schemes. However, for certain distributions described by both a shape and a scale parameter, random sampling led to estimators that were inconsistent. On the other hand, the estimates obtained from inverse sampling were always consistent. Moreover, for moderate sized record-breaking samples, the total sample size that needs to be observed is smaller for inverse sampling than for random sampling.
record-breaking random sampling inverse sampling efficiency mean square errors