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Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2021 / Cilt: 11 - Sayı: 1

Parameter Estimation on Geometric Distribution of Order k with Different Reward Laws

Fatih ŞAHİN
Coşkun KUŞ
İsmail KINACI
Kadir KARAKAYA
Yunus AKDOĞAN
Pages
23–47
Publication Date
2021-06-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Proportion estimates are also discussed for distribution of with geometric rewards.

📌 3 Key Takeaways

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Objective & Hypothesis:Let $\ksi1, \ksi2, ....$ be a sequence of independent trials with two possible outcomes, “0” and “1” where “1” represents the success of Type-I, and “0” denotes the success of Type-II.
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Key Findings & Data:The geometric distributed rewards are studied by Eryılmaz et al. in [1].
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Conclusion & Impact:Proportion estimates are also discussed for distribution of with geometric rewards.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Geometric distribution of order k · Bernoulli reward · Exponential reward

Abstract

Let $\ksi1, \ksi2, ....$ be a sequence of independent trials with two possible outcomes, “0” and “1” where “1” represents the success of Type-I, and “0” denotes the success of Type-II. For nonnegative integers kr and kl using a reward scheme, we obtained the distribution of the number of trials (W) until the sum of consecutive rewards of Type-I is equal to or exceeds the level kr, or the sum of consecutive rewards of Type-II is equal to or exceeds the level kl. The geometric distributed rewards are studied by Eryılmaz et al. in [1]. In this study, the survival function of W is obtained for binary sequence with Bernoulli and exponential rewards as well as geometric rewards. A simulation study is performed to compare the theoretical and simulated probabilities. Proportion estimates are also discussed for distribution of with geometric rewards.

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Cite This Article

ŞAHİN, F., KUŞ, C., KINACI, İ., KARAKAYA, K., AKDOĞAN, Y. (2021). Parameter Estimation on Geometric Distribution of Order k with Different Reward Laws. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 11 - Sayı: 1, 23–47. https://ajindex.com/articles/451024

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References (7)

  1. Eryılmaz, S., Gong, M., Xie, M., Generalized sooner waiting time problems in a sequence of trinary trials, Statistics and probability Letters, 115, 70-78, 2016
  2. Philippou, A.N., Georghiou, C., Philippou, G.N., A generalized geometric distribution and some of its properties, Statistics and probability Letters, 1, 171-175, 1983
  3. Eryılmaz, S., Geometric distribution of order k with a reward, Statistics and probability Letters, 92, 53-58, 2014
  4. Koutras, M.V., Alexandrou, V.A., Sooner waiting time problems in a sequence of trinary trials, Journal Applied Probability, 34, 593-609, 1997
  5. Demir, S., Eryılmaz, S., Run statistics in a sequence of arbitrarily dependent binary trials, Statistical Papers, 51(4), 959-973, 2010
  6. Mallor, F., Santos, J., Reliability of systems subject to shocks with a stochastic dependence for the damages, Sociedad de Estadistica e Investigacion Opevativa Test, 12(2), 427-444, 2003
  7. Khan, M.A., Khalique, A., Abouammoh, A.M., On estimating parameters in a discrete Weibull distribution, IEEE Transactions on Reliability, 38(3), 348-350, 1989.