A new estimator for stationary distribution of the inventory model of type (s, S)
We consider inventory model of type (s, S) which is used mostly in stock control policy. It is very important to know characteristics of an inventory model of type (s, S), such as stationary distribution. Using the straight line approach of Frees (1986a), we establish estimator for ergodic distribution of inventory model of type (s, S) and investigate asymptotic properties of this estimator such as consistency, asymptotic unbiasedness and asymptotic normality.
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Proof. The covariance between X k and X m is obtained as follows: ( ) ( E X Cov X,Xm= k, ) ( ) k k m. Xm− µm =E X Xm− µ µ. Here E X X m k term is obtained as