When trying to apply the former described methods to practical historical
data, one has ever to cope with the following fact: the actual demand
cannot be observed with precision when the demand overflows the inventory.
The useful parameters, namely 
,
must therefore be estimated by recreating the missing data. And this
cannot be done either "distribution free" nor cost
free.
For this reason, it is of interest to compute the value of the missing
informations. It is known that, for moderate 
and fixed 
and 
, an information concerning the shape of the distribution
has a negligible value.
On the opposite, if you are playing against the set of the "two Dirac's", the value of an information relative to which is the right measure of the dispersion is significantly greater than those relative to the shape.
All these values are to be compared to the value associated with the
uncertainty concerning the mean that is generated by the limited
size of the historical data.
Some results have been obtained concerning the sample distribution
of the intermeans parameter 
. Part of them have been proved,
while some other are only conjectures based on numerical simulations.
Especially, the ways to obtain a non biased estimator of this parameter
are investigated.
In any case, this study is unavoidable when trying to estimate the
parameter of the distribution from the corresponding value
extracted from a small sized set of historical data.