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

Esra Gokpinar, Tahir Khaniyev, Hamza Gamgam, Fikri Gokpinar
1.834 449

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.


Keywords


Inventory model of type (s, S), Ergodic distribution, Estimation, Consistency, Asymptotic unbiasedness, Asymptotic normality.

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References


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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