A semi-Markovian renewal reward process with Γ(g) distributed demand

KESEMEN, Tülay; Alakoç, Büşra; KHANIYEV, Tahir; KAMIŞLIK, Aslı BEKTAŞ

doi:10.3906/mat-2002-72

A semi-Markovian renewal reward process with Γ(g) distributed demand

Aslı BEKTAŞ KAMIŞLIK, (Recep Tayyip Erdoğan Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, Rize, Türkiye)

Büşra ALAKOÇ, (Karadeniz Teknik Üniversitesi, Fen Fakültesi, Matematik Bölümü, Trabzon, Türkiye)

Tülay KESEMEN, (Karadeniz Teknik Üniversitesi, Fen Fakültesi, Matematik Bölümü, Trabzon, Türkiye)

Tahir KHANIYEV (TOBB Ekonomi ve Teknoloji Üniversitesi, Mühendislik Fakültesi, Endüstri Mühendisliği Bölümü, Ankara, Türkiye)

Turkish Journal of Mathematics

3 0

Yıl: 2020 Cilt: 44 Sayı: 4 Sayfa Aralığı: 1250 - 1262 Metin Dili: İngilizce DOI: 10.3906/mat-2002-72 İndeks Tarihi: 28-08-2020

A semi-Markovian renewal reward process with Γ(g) distributed demand

Öz:

We consider a classical semi-Markovian stochastic model of type (s, S) with Logistic distributed demandrandom variables. Logistic distribution is a member of special distribution class known as Γ(g) that encounters inmany real-life applications involving extreme value theory. The objective of this study is to observe some majorcharacteristics of a stochastic process X(t) which represents semi-Markovian renewal reward process of type (s, S).We used new approximation results for renewal function that allow us to obtain three-term asymptotic expansion forergodic distribution function and for $n^{th}$ order moments of ergodic distribution of the process X(t).

Anahtar Kelime:

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[1] Aliyev RT. Asymptotic expansions for the some probability characteristics of the one stochastic process with a heavy tailed distributed component having finite variance. Journal of Contemporary Applied Mathematics 2018; 8 (1): 51-61.
[2] Aliyev RT, Ardıç Ö, Khaniyev T. Asymptotic approach for a renewal-reward process with a general interference of chance. Communication in Statistics: Theory and Methods 2016; 45 (16): 4237-4248.
[3] Aliyev RT. On a stochastic process with a heavy-tailed distributed component describing inventory model type of (s,S). Communication in Statistics: Theory and Methods 2016; 46 (5): 2571-2579.
[4] Aliyev RT, Küçük Z, Khaniyev T. Three-term asymptotic expansions for the moments of the random walk with triangular distributed interference of chance. Applied Mathematical Modelling 2010; 34 (11): 3599-3607.
[5] Anderson KK, Athreya KB. A Renewal theorem in the infinite mean case. The Annals of Probability 1987; 88 (15): 388-393.
[6] Bektaş KA, Kesemen T, Khaniyev T. Inventory model of type (s,S) under heavy tailed demand with infinite variance. Brazilian Journal of Probability and Statistics 2019; 33 (1): 39-56.
[7] Bektaş KA, Kesemen T, Khaniyev T. On the moments for ergodic distribution of an inventory model of type (s,S) with regularly varying demands having infinite variance. TWMS Journal of Applied and Engineering Mathematics 2018; 8 (1a): 318-329.
[8] Bektaş KA, Kesemen T, Khaniyev T. The class of L ∩ D and its application to renewal reward process. AIP Conference Proceedings 2018; 1926 (1). doi:10.1063/1.5020457.
[9] Geluk JL, Frenk JBG. Renewal theory for random variables with a heavy tailed distribution and finite variance. Statistics and Probability Letters 2011; 81: 77-82.
[10] Geluk JL, Haan LD. Stable probability distributions and their domains of attraction: a direct approach. Probability and Mathematical Statistics 2009; 20 (1): 169-188.
[11] Geluk JL. A renewal theorem in the finite-mean case. Proceedings of the American Mathematical Society 1992; 125 (11): 3407-3413.
[12] Hanalioglu Z, Fescioglu Unver N., Khaniyev T. Asymptotic expansions for the moments of the renewal-reward process with a normal distributed interference of chance. Applied and Computational Mathematics 2018; 17 (2): 141-150.
[13] Khaniyev T, Kokangul A, Aliyev RT. An asymptotic approach for a semi-Markovian inventory model of type (s,S). Applied Stochastic Models in Business and Industry 2013; 29(5): 439-453.
[14] Khaniyev T, Aksop C. Asymptotic results for an inventory model of type (s,S) with a generalized Beta interference of chance. TWMS Journal of Applied and Engineering Mathematics 2011; 2 (1): 223-236.
[15] Khaniyev T, Atalay KD. On the weak convergence of the ergodic distribution for an inventory model of type (s,S). Hacettepe Journal of Mathematics and Statistics 2010; 9 (4): 599-611.
[16] Khaniyev TA, Mammadova Z. On the stationary characteristics of the extended model of type (s,S) with Gaussian distribution of summands. Journal of Statistical Computation and Simulation 2006; 76 (10): 861-874.
[17] Kesemen T, Bektaş KA, Küçük Z, Şenol E. Inventory model of type (s,S) with subexponential Weibull distributed demand. Journal of the Turkish Statistical Association 2016; 9(3): 81-92.
[18] Mitov KV, Omey E. Intuitive approximations for the renewal function. Statistics and Probability Letters 2014; 84: 72-80.
[19] Nasirova, TI, Yapar C, Khaniev TA. On the probability characteristics of the stock level in the model of type (s, S). Cybernetics and System Analysis 1998; 5: 69-76.

APA	KAMIŞLIK A, Alakoç B, KESEMEN T, KHANIYEV T (2020). A semi-Markovian renewal reward process with Γ(g) distributed demand. , 1250 - 1262. 10.3906/mat-2002-72
Chicago	KAMIŞLIK Aslı BEKTAŞ,Alakoç Büşra,KESEMEN Tülay,KHANIYEV Tahir A semi-Markovian renewal reward process with Γ(g) distributed demand. (2020): 1250 - 1262. 10.3906/mat-2002-72
MLA	KAMIŞLIK Aslı BEKTAŞ,Alakoç Büşra,KESEMEN Tülay,KHANIYEV Tahir A semi-Markovian renewal reward process with Γ(g) distributed demand. , 2020, ss.1250 - 1262. 10.3906/mat-2002-72
AMA	KAMIŞLIK A,Alakoç B,KESEMEN T,KHANIYEV T A semi-Markovian renewal reward process with Γ(g) distributed demand. . 2020; 1250 - 1262. 10.3906/mat-2002-72
Vancouver	KAMIŞLIK A,Alakoç B,KESEMEN T,KHANIYEV T A semi-Markovian renewal reward process with Γ(g) distributed demand. . 2020; 1250 - 1262. 10.3906/mat-2002-72
IEEE	KAMIŞLIK A,Alakoç B,KESEMEN T,KHANIYEV T "A semi-Markovian renewal reward process with Γ(g) distributed demand." , ss.1250 - 1262, 2020. 10.3906/mat-2002-72
ISNAD	KAMIŞLIK, Aslı BEKTAŞ vd. "A semi-Markovian renewal reward process with Γ(g) distributed demand". (2020), 1250-1262. https://doi.org/10.3906/mat-2002-72

APA	KAMIŞLIK A, Alakoç B, KESEMEN T, KHANIYEV T (2020). A semi-Markovian renewal reward process with Γ(g) distributed demand. Turkish Journal of Mathematics, 44(4), 1250 - 1262. 10.3906/mat-2002-72
Chicago	KAMIŞLIK Aslı BEKTAŞ,Alakoç Büşra,KESEMEN Tülay,KHANIYEV Tahir A semi-Markovian renewal reward process with Γ(g) distributed demand. Turkish Journal of Mathematics 44, no.4 (2020): 1250 - 1262. 10.3906/mat-2002-72
MLA	KAMIŞLIK Aslı BEKTAŞ,Alakoç Büşra,KESEMEN Tülay,KHANIYEV Tahir A semi-Markovian renewal reward process with Γ(g) distributed demand. Turkish Journal of Mathematics, vol.44, no.4, 2020, ss.1250 - 1262. 10.3906/mat-2002-72
AMA	KAMIŞLIK A,Alakoç B,KESEMEN T,KHANIYEV T A semi-Markovian renewal reward process with Γ(g) distributed demand. Turkish Journal of Mathematics. 2020; 44(4): 1250 - 1262. 10.3906/mat-2002-72
Vancouver	KAMIŞLIK A,Alakoç B,KESEMEN T,KHANIYEV T A semi-Markovian renewal reward process with Γ(g) distributed demand. Turkish Journal of Mathematics. 2020; 44(4): 1250 - 1262. 10.3906/mat-2002-72
IEEE	KAMIŞLIK A,Alakoç B,KESEMEN T,KHANIYEV T "A semi-Markovian renewal reward process with Γ(g) distributed demand." Turkish Journal of Mathematics, 44, ss.1250 - 1262, 2020. 10.3906/mat-2002-72
ISNAD	KAMIŞLIK, Aslı BEKTAŞ vd. "A semi-Markovian renewal reward process with Γ(g) distributed demand". Turkish Journal of Mathematics 44/4 (2020), 1250-1262. https://doi.org/10.3906/mat-2002-72