### A new estimator for stationary distribution of the inventory model of type (s, S)

#### Abstract

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