ABSTRACT
When they exist, estimates ~ and e can be found as the simultaneous solution of these two equations. However, no solution exists when (i) all sample observations are k's, in which case nk = N, nk+ 1 = 0, and x = k, and (ii) all sample observations are k + 1, in which case nk = 0, nk+ 1 = N, and x = k + 1. In the event that nk = nk+ 1 = 0, no estimate exists fore, but the first equation of (14.2.3) leads to the estimate X. = x. Although these exceptional cases are of theoretical interest, they are not likely to be of any practical importance unless samples are small, and it is not expected that these estimators will be employed unless samples are reasonably large. The occurrence of samples for which acceptable estimates of A. and e fail to exist should be viewed as a suggestion that perhaps the probability function of ( 14. 2.1) is not applicable to the random variable actually being observed.
