Abstract. In this paper, we study the nonunit mass of the gamma (gamma and the modified gamma) kernels estimator for the finite samples. For this, we propose to use the normalization approach (Macro-normalization and the Micro-Normalization) to correct the problem of the nonunit mass. In the aim to illustrate the necessity of the normalization approach a detailed simulation study investigates the local and global performances of the considered estimators. The obtained results show the good performances of the normalized gamma kernels estimators.Résumé. Dans ce papier, nous avons abordé le problème de la non conservation de masse des estimateursà noyaux gamma (gamma et gamma modifié) pour deséchantillons finis. Pour cela, deux approches (Macro-normalisation et Micro-normalisation) ontété proposées pour remédierà ce problème. Afin d'illustrer la nécessité de ces approches, uneétude de comparaison par simulation aété réalisée. Par conséquent, les résultats obtenus montrent qu'il est préférable d'utiliser les estimateursà noyaux gamma normalisés.
We consider a single server Markovian feedback queue with variant of multiple
vacation policy, balking, server's states-dependent reneging, and retention
of reneged customers. We obtain the steady-state solution of the considered
queue based on the use of probability generating functions. Then, the
closed-form expressions of different system characteristics are derived.
Finally, we present some numerical results in order to show the impact of the
parameters of impatience timers on the performance measures of the system.
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