K. S. Sultan

Comparison of estimates using record statistics from Weibull model: Bayesian and non-Bayesian approaches

This paper develops a Bayesian analysis in the context of record statistics values from the two-parameter Weibull distribution. The ML and the Bayes estimates based on record values are derived for the two unknown parameters and some survival time parameters e.g. reliability and hazard functions. The Bayes estimates are obtained based on a conjugate prior for the scale parameter and a discrete prior for the shape parameter of this model. This is done with respect to both symmetric loss function (squared error loss), and asymmetric loss function (linear-exponential (LINEX)) loss function. The maximum likelihood and the different Bayes estimates are compared via a Monte Carlo simulation study. A practical example consisting of real record values using the data from an accelerated test on insulating fluid reported by Nelson was used for illustration and comparison. Finally, Bayesian predictive density function, which is necessary to obtain bounds for predictive interval of future record is derived and discussed using a numerical example. The results may be of interest in a situation where only record values are stored.

Mixture of two inverse Weibull distributions: Properties and estimation

The mixture model of two Inverse Weibull distributions (MTIWD) is investigated. First, some properties of the model with some graphs of the density and hazard function are discussed. Next, the identifiability property of the MTIWD is proved. In addition, the estimates of the unknown parameters via the EM Algorithm are obtained. The performance of the findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulations.

Bayesian and maximum likelihood estimations of the inverse Weibull parameters under progressive type-II censoring

In this paper, the statistical inference of the unknown parameters of a two-parameter inverse Weibull (IW) distribution based on the progressive type-II censored sample has been considered. The maximum likelihood estimators (MLEs) cannot be obtained in explicit forms, hence the approximate MLEs are proposed, which are in explicit forms. The Bayes and generalized Bayes estimators for the IW parameters and the reliability function based on the squared error and Linex loss functions are provided. The Bayes and generalized Bayes estimators cannot be obtained explicitly, hence Lindleys approximation is used to obtain the Bayes and generalized Bayes estimators. Furthermore, the highest posterior density credible intervals of the unknown parameters based on Gibbs sampling technique are computed, and using an optimality criterion the optimal censoring scheme has been suggested. Simulation experiments are performed to see the effectiveness of the different estimators. Finally, two data sets have been analysed for illustrative purposes.

Estimation and prediction from gamma distribution based on record values

In this paper, we introduce the record values arising from gamma distribution with three parameters. Next, we compute the means, variances and covariances of the lower record values. Then, we use these moments to calculate the best linear unbiased estimates (BLUEs) for the location and scale parameters of gamma distribution. By using the BLUEs, we construct confidence intervals for the location and scale parameters through Monte Carlo simulations. In addition, we discuss the point and interval prediction for the future records.

Order Statistics from the Generalized Exponential Distribution and Applications

Recently, a new distribution, called generalized exponential distribution (GED), has been introduced and studied quite extensively by authors. The GED can be used as an alternative to gamma and Weibull distributions in many situations. In this article, we use the moments of order statistics from the GED derived by Raqab and Ahsanullah (2001) and Raqab (2004) to develop the correlation goodness -of-fit test for the GED. In addition, we calculate the power of the test based on some other alternative distributions. Further, we construct approximate confidence intervals for the location and scale parameters of the GED. Finally, we apply the procedures developed in the paper to real data set.

Order statistics from inverse Weibull distribution and associated inference

Order statistics arising from inverse Weibull (IW) distribution are considered. Exact expression for the single moments of order statistics are derived. Also, the variances and covariances are calculated. Based on the moments of order statistics, the best linear unbiased estimates (BLUEs) for the location and scale parameters of IW distribution are obtained. In addition, these BLUEs are applied to draw inferences for the location and scale parameters of the underlying model. To show the usefulness of our results a simulation study is carried out.

Parametric and nonparametric estimation of P(Y < X) for finite mixtures of lognormal components

In this paper, parametric and nonparametric estimators of the stressstrength reliability are obtained and compared when the random variables X and Y are independent and each of which is a mixture of lognormal components. 100(1 - α)% confidence bounds are obtained and compared in both of the parametric and nonparametric cases. Sin~ulation shows that the parametric point estimates are better than the nonparametric point estimates for all sample sizes. This is also true for interval estimates. particularly when the sample size N is small. As N increases: no great loss in precision occurs if Goviildarajulus bounds arc used rather than the parametric bounds. The nonparanietric bounds are simpler and faster to obtain.

Bayesian Estimates Based on Record Values from the Inverse Weibull Lifetime Model

Abstract In this paper, we use the lower record values from the inverse Weibull distribution (IWD) to derive and discuss different methods of estimation in two different cases, (i) when the shape parameter is known and (ii) when both of the shape and scale parameters are unknown. First, we discuss the maximum likelihood estimates. Next, we derive the Bayes estimates based on different loss functions. Also, we obtain the estimates of the reliability and hazard functions. In order to compare the different estimates we calculate the mean square errors through Monte Carlo simulations. Finally, we apply the findings of the paper to some simulated data.

Order statistics from the doubly truncated linear-exponential distribution and its characterizations

In this paper single and product moments of order statistics from the doubly truncated linear-exponential distribution are studied. Some recurrence relations for both single and product moments of order statistics are also derived. Two results for characterizing the linear-exponential distribution through the properties of order statistics are also presented.

Two-sample Bayesian prediction for sequential order statistics from exponential distribution based on multiply Type-II censored samples

In this paper, the problem of predicting the future sequential order statistics based on observed multiply Type-II censored samples of sequential order statistics from one- and two-parameter exponential distributions is addressed. Using the Bayesian approach, the predictive and survival functions are derived and then the point and interval predictions are obtained. Finally, two numerical examples are presented for illustration.