Estimating the demand distributions of single-period items having frequent stockouts

Very often, the service level of a single-period newsboy-type product is set at such a low level that: (i) stockouts occur in the majority of the periods, and (ii) a large right-hand side of the empirical demand distribution is never observable. This paper reports a practical approach for estimating the periodic-demand distribution of such a product. The approach has three components: (i) using the non-parametric ‘product limit’ method to estimate the fractiles of the observable left-hand side of the empirical distribution; (ii) using a subjective approach and an ‘extrapolation of hourly sales’ approach to ‘fill in’ the missing right-hand side of the empirical distribution; (iii) fitting the estimates obtained in the preceding two components to a Tocher curve — which can handle the diversity of shapes of a realistic demand distribution and is also computationally very convenient for subsequent calculations for production/inventory decisions. The entire approach is shown to be simpler but more powerful than existing alternatives for the problem.