The main purpose of this paper is to obtain estimates of parameters, reliability and hazard rate functions of a heterogeneous population represented by finite mixture of two general components. The doubly Type II censoring of generalized order statistics scheme is used. Maximum likelihood and Bayes methods of estimation are used for this purpose. The two methods of estimation are compared via a Monte Carlo Simulation study
The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerated life tests are applied based on progressively type-II censored samples. The maximum likelihood estimates (MLEs) for the considered parameters are obtained by solving the likelihood equations of the model parameters numerically. The Bayes estimators are obtained by using Markov chain Monte Carlo algorithm under the balanced squared error loss function. Based on Monte Carlo simulation, Bayes estimators are compared with their corresponding maximum likelihood estimators. The two-sample prediction technique is considered to derive Bayesian prediction bounds for future order statistics based on progressively type-II censored informative samples obtained from constant-partially accelerated life testing models. The informative and future samples are assumed to be obtained from the same population. The coverage probabilities and the average interval lengths of the confidence intervals are computed via a Monte Carlo simulation to investigate the procedure of the prediction intervals. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.
This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values. Numerical example is presented in the methods proposed in this paper
This paper is concerned with the problem of obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two exponentiated Weibull (MTEW) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values.
This article is concerned with the problem of prediction for the future generalized order statistics from a mixture of two general components based on doubly type II censored sample. We consider the one sample prediction and two sample prediction techniques. Bayesian prediction intervals for the median of future sample of generalized order statistics having odd and even sizes are obtained. Our results are specialized to ordinary order statistics and ordinary upper record values. A mixture of two Gompertz components model is given as an application. Numerical computations are given to illustrate the procedures.
This article is concerned with the problem of estimating the parameters, reliability and hazard rate functions of the mixture of two Rayleigh distributions (MT RD) based on generalized order statistics (GOS ). The maximum likelihood and Bayes methods of estimation are used for this purpose. The Markov chain Monte Carlo (MCMC) method is used for obtaining the Bayes estimates under the squared error loss and LINEX loss functions. Our results are specialized to progressive Type-II censored order statistics and upper record values. Comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.
In this article, we establish some recurrence relations for both single and product moments of progressively Type-II right censored order statistics from the complementary exponential-geometric distribution. For a particular case, these relations are reduced to the corresponding results for the usual order statistics due to Balakrishnan et al. (J Stat Comput Simul 85(11): 2187-2201, 2015. Then we use these moments to obtain the best linear unbiased estimators of the scale and location-scale parameters of the complementary exponentialgeometric distribution based on progressively Type-II right censored samples. Further, we discuss the best linear unbiased predictors of future failure times. Finally, an example is presented to show the application of our results.
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