An estimation procedure for the disposition of fitting parts

This article deals with the estimation of the functional parameters of a (normal-)distribution from grouped samples. In contrast to the well-known problem, in the present investigation the data are classified into several non-contiguous and overlapping intervals (i.e., the classes are not mutually exclusive). Therefore, conventional methods cannot be applied. Of course, this grouping is not done intentionally, but is due to certain ‘production requirements’. Two methods, based on maximum-likelihood and minimum-&chi², are derived in order to handle this awkward situation and to render an estimation possible. Numerical results of a simulation study show that both methods lead to fair results, provided that the sample size is large enough.