In this paper, the problem of estimating the parameter of Akash distribution applied when the lifetime of the product follow Type-Ⅱ censoring. The maximum likelihood estimators (MLE) are studied for estimating the unknown parameter and reliability characteristics. Approximate confidence interval for the parameter is derived under the s-normal approach to the asymptotic distribution of MLE. The Bayesian inference procedures have been developed under the usual error loss function through Lindley's technique and Metropolis-Hastings algorithm. The highest posterior density interval is developed by using Metropolis-Hastings algorithm. Finally, the performances of the different methods have been compared through a Monte Carlo simulation study. The application to set of real data is also analyzed using proposed methods.
Citation: Tahani A. Abushal. Parametric inference of Akash distribution for Type-Ⅱ censoring with analyzing of relief times of patients[J]. AIMS Mathematics, 2021, 6(10): 10789-10801. doi: 10.3934/math.2021627
In this paper, the problem of estimating the parameter of Akash distribution applied when the lifetime of the product follow Type-Ⅱ censoring. The maximum likelihood estimators (MLE) are studied for estimating the unknown parameter and reliability characteristics. Approximate confidence interval for the parameter is derived under the s-normal approach to the asymptotic distribution of MLE. The Bayesian inference procedures have been developed under the usual error loss function through Lindley's technique and Metropolis-Hastings algorithm. The highest posterior density interval is developed by using Metropolis-Hastings algorithm. Finally, the performances of the different methods have been compared through a Monte Carlo simulation study. The application to set of real data is also analyzed using proposed methods.
| [1] | R. Shanker, Akash distribution and its applications, Int. J. Probab. Statist., 4 (2015), 65–75. |
| [2] | R. Shanker, H. Fesshay, S. Selvaraj, On modeling of lifetime data using one parameter Akash, Lindley and exponential distributions, Biom. Biostat. Int. J., 3 (2016), 56–62. |
| [3] | R. Shanker, K. K. Shukla, On two-parameter Akash distributions, Biom. Biostat. Int. J., 6 (2017), 416–425. |
| [4] | R. Shanker, K. K. Shukla, R. Shanker, A. Pratap, A generalized Akash distributions, Biom. Biostat. Int. J., 7 (2018), 18–26. |
| [5] |
T. A. Abushal, Bayesian estimation of the reliability characteristic of Shanker distribution, J. Egyptian Math. Soc., 27 (2019), 1–15. doi: 10.1186/s42787-019-0001-5
|
| [6] |
A. C. Cohen, Maximum Likelihood Estimation in the Weibull Distribution Based on Complete and Censored Samples, Technometrics, 7 (1965), 579–588. doi: 10.1080/00401706.1965.10490300
|
| [7] | J. F. Lawless, Statistical models and methods for lifetime data, John Wiley & Sons, 2003. |
| [8] |
B. Pradhan, D. Kundu, On progressively censored generalized exponential distribution, Test, 18 (2009), 497–515. doi: 10.1007/s11749-008-0110-1
|
| [9] |
D. Kundu, B. Pradhan, Bayesian inference and life testing plans for generalized exponential distribution, Sci. China Ser. A, 52 (2009), 1373–1388. doi: 10.1007/s11425-009-0085-8
|
| [10] | D. V. Lindley, Approximate Bayesian Method, Trabajos de estadística y de investigación operativa, 31 (1980), 223–245. |
| [11] |
W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57 (1970), 97–109. doi: 10.1093/biomet/57.1.97
|
| [12] |
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, Equations of state calculations by fast computing machines, J. Chem. Phys., 21 (1953), 1087–1092. doi: 10.1063/1.1699114
|
| [13] | M. H. Chen, Q. M. Shao, Monte Carlo estimation of Bayesian credible and HPD intervals, J. Comput. Graph. Stat., 8 (1999), 69–92. |
| [14] | A. J. Gross, V. Clark, Survival distributions: Reliability applications in the biometrical sciences, John Wiley & Sons, 1975. |
| [15] |
E. K. AL-Hussaini, A. H. Abdel-Hamid, Bayesian estimation of the parameters, reliability and hazard rate functions of mixtures under accelerated life tests, Commun. Stat. Simul. C., 33 (2004), 963–982. doi: 10.1081/SAC-200040703
|
| [16] |
L. Tierney, J. B. Kadane, Accurate approximations for posterior moments and marginal densities, J. Am. Stat. Assoc., 81 (1986), 82–86. doi: 10.1080/01621459.1986.10478240
|
Tahani A. Abushal. Parametric inference of Akash distribution for Type-Ⅱ censoring with analyzing of relief times of patients[J]. AIMS Mathematics, 2021, 6(10): 10789-10801. doi: 10.3934/math.2021627
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