  The newsvendor problem is a popular inventory management problem in supply
chain management and logistics. Solutions to the newsvendor problem determine
optimal inventory levels. This model is typically fully determined by a
purchase and sale prices and a distribution of random market demand. From a
statistical point of view, this problem is often considered as a quantile
estimation of a critical fractile which maximizes anticipated profit. The
distribution of demand is a random variable and is often estimated on historic
data. In an ideal situation, when the probability distribution of the demand is
known, one can determine the quantile of a critical fractile minimizing a
particular loss function. Since maximum likelihood estimation is asymptotically
efficient, under certain regularity assumptions, the maximum likelihood
estimators are used for the quantile estimation problem. Then, the Cramer-Rao
lower bound determines the lowest possible asymptotic variance. Can one find a
quantile estimate with a smaller variance then the Cramer-Rao lower bound? If a
relevant additional information is available then the answer is yes. Additional
information may be available in different forms. This manuscript considers
minimum variance and minimum mean squared error estimation for incorporating
additional information for estimating optimal inventory levels. By a more
precise assessment of optimal inventory levels, we maximize expected profit
