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

Öz

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.

Anahtar Kelimeler

• Geometric distribution of order k
• Bernoulli reward
• Exponential reward
• Estimation

Kaynakça

1. [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. [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. [3] Eryılmaz, S., Geometric distribution of order k with a reward, Statistics and probability Letters, 92, 53-58, 2014.
4. [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. [5] Demir, S., Eryılmaz, S., Run statistics in a sequence of arbitrarily dependent binary trials, Statistical Papers, 51(4), 959-973, 2010.
6. [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. [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.