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

Authors : Fatih ŞAHİN, Coşkun KUŞ, İsmail KINACI, Kadir KARAKAYA, Yunus AKDOĞAN

Pages : 23-47

Doi:10.37094/adyujsci.873193

View : 21 | Download : 15

Publication Date : 2021-06-30

Article Type : Research Paper

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.
Keywords : Geometric distribution of order k, Bernoulli reward, Exponential reward, Estimation