In this paper, the geometric distribution parameter is estimated under a type-I censoring scheme by means of the Bayesian estimation approach. The Beta and Kumaraswamy informative priors, as well as five loss functions are used for this purpose. Expressions of Bayes estimators and Bayes risks are derived under the Squared Error Loss Function (SELF), the Quadratic Loss Function (QLF), the Precautionary Loss Function (PLF), the Simple Asymmetric Precautionary Loss Function (SAPLF), and the DeGroot Loss Function (DLF) using the two aforementioned priors. The prior densities are obtained through prior predictive distributions. Simulation studies are carried out to make comparisons using Bayes risks. Finally, a real-life data example is used to verify the model’s efficiency.
prior distribution, posterior distribution, geometric distribution, beta distribution, Kumraswamy distribution.
Abbas, K., Hussain, Z., Rashid, N., Ali, A., Taj, M., Khan, S.A., Manzoor, S., Khalil, U. and Khan, D. M., (2020). Bayesian estimation of gumbel type-II distribution under type-II censoring with medical applicatioNs. Computational and Mathematical Methods in Medicine , pp. 1–11.
Aslam, M., (2003). An application of prior predictive distribution to elicit the prior density. Journal of Statistical Theory and applications, 2(1), pp. 70–83.
Khan, A. A., Aslam, M., Hussain, Z., & Tahir, M., (2015). Comparison of loss functions for estimating the scale parameter of log-normal distribution using non-informative priors. Hacettepe Journal of Mathematics and Statistics, 45(6), pp. 1831–1845.
Kour, K., Kumar, P., Anand, P., &Sudan, J. K., (2020). E-Bayesian estimation of Exponential- Lomax distribution under asymmetric loss functions. International Journal of Applied Mathematics and Statistics, Int. J. Appl. Math. Stat., 59(2), pp. 1–26.
Krishna, H., & Goel, N., (2017). Maximum likelihood and Bayes estimation in randomly censored geometric distribution. Journal of Probability and Statistics, 3, pp. 1–12.
Long, B., (2021). Estimation and prediction for the Rayleigh distribution based on double type-I hybrid censored data. Communications in Statistics-Simulation and Computation, pp. 1–15.
Saleem, M., Aslam, M., & Economou, P., (2010). On the Bayesian analysis of the mixture of power function distribution using the complete and the censored sample. Journal of Applied Statistics, 37(1), pp. 25–40.
Shi, Y., & Yan, W., (2010). The EB estimation of scale-parameter for two parameter exponential distribution under the type-I censoring life test, Journal of Physical Science, 4, pp. 25–30.
Tahir, M., Aslam, M., & Hussain, Z., (2016). On the Bayesian analysis of 3-component mixture of exponential distributions under different loss functions. Hacettepe Journal of Mathematics and Statistics, 45(2), pp. 609–628.
Yanuar, F., Yozza, H., & Rescha, R. V., (2019). Comparison of two priors in Bayesian estimation for parameter of Weibull distribution. Science and Technology Indonesia, 4(2), pp. 82–87.