Amal Helu

Estimation of the inverse Weibull distribution based on progressively censored data: Comparative study

Abstract In this article we consider statistical inferences about the unknown parameters of the Inverse Weibull distribution based on progressively type-II censoring using classical and Bayesian procedures. For classical procedures we propose using the maximum likelihood; the least squares methods and the approximate maximum likelihood estimators. The Bayes estimators are obtained based on both the symmetric and asymmetric ( Linex , General Entropy and Precautionary) loss functions. There are no explicit forms for the Bayes estimators, therefore, we propose Lindley׳s approximation method to compute the Bayes estimators. A comparison between these estimators is provided by using extensive simulation and three criteria, namely, Bias, mean squared error and Pitman nearness ( PN ) probability. It is concluded that the approximate Bayes estimators outperform the classical estimators most of the time. Real life data example is provided to illustrate our proposed estimators.

Bayes Estimation of Weibull Distribution Parameters Using Ranked Set Sampling

Estimation of the parameters of Weibull distribution is considered using different methods of estimation based on different sampling schemes namely, Simple Random Sample (SRS), Ranked Set Sample (RSS), and Modified Ranked Set Sample (MRSS). Methods of estimation used are Maximum Likelihood (ML), Method of moments (Mom), and Bayes. Comparison between estimators is made through simulation via their Biases, Relative Efficiency (RE), and Pitman Nearness Probability (PN). Estimators based on RSS and MRSS have many advantages over those that are based on SRS.

A nonparametric test of symmetry based on the overlapping coefficient

In this paper, we introduce a new nonparametric test of symmetry based on the empirical overlap coefficient using kernel density estimation. Our investigation reveals that the new test is more powerful than the runs test of symmetry proposed by McWilliams [31]. Intensive simulation is conducted to examine the power of the proposed test. Data from a level I Trauma center are used to illustrate the procedures developed in this paper.

Estimation on Lomax Progressive Censoring Using the EM Algorithm

Based on progressively type-II censored data, the maximum-likelihood estimators (MLEs) for the Lomax parameters are derived using the expectation–maximization (EM) algorithm. Moreover, the expected Fisher information matrix based on the missing value principle is computed. Using extensive simulation and three criteria, namely, bias, root mean squared error and Pitman closeness measures, we compare the performance of the MLEs via the EM algorithm and the Newton–Raphson (NR) method. It is concluded that the EM algorithm outperforms the NR method in all the cases. Two real data examples are used to illustrate our proposed estimators.

Estimation of Sib–Sib Correlation via a Kotz-Type Density Function

We estimate sib–sib correlation by maximizing the log-likelihood of a Kotz-type distribution. Using extensive simulations we conclude that estimating sib–sib correlation using the proposed method has many advantages. Results are illustrated on a real life data set due to Galton. Testing of hypothesis about this correlation is also discussed using the three likelihood based tests and a test based on Srivastavas estimator. It is concluded that score test derived using Kotz-type density performs the best.

On Inference of Overlapping Coefficients in Two Lomax Populations Using Different Sampling Methods

This paper investigates point and interval estimation for some well-known measures of overlap. Two types of sampling procedures, namely, Simple Random Sample and Ranked Set Sample from two Lomax populations with different shape parameters are considered. Simulation studies are conducted to get insight on the performance of the proposed estimators. Taylor series approximations as well as bootstrap method are used to construct confidence intervals for those measures.

Distribution-Free Runs Test for Conditional Symmetry

A distribution-free runs test for conditional symmetry is proposed. The null distribution of the test statistics is derived. Intensive simulation is conducted to examine the power of the proposed test for different sample sizes and different alternatives. Data on the bilirubin level of babies in neonatal intensive care is used to illustrate the method.

On estimation of overlapping measures for exponential populations under progressive first failure censoring

Abstract Overlapping coefficient is a direct measure of similarity between two distributions which is recently becoming very useful in many fields of applications including microarray analysis for the purpose of identifying differentially expressed biomarkers, especially in case when data follow multimodal distribution. However, inferences on overlapping coefficient are quite limited especially under different sampling schemes including censored data. In this article we consider a life test scheme called a progressive first-failure censoring scheme introduced by Wu and Kuş (2009). Based on this type of censoring, we draw inference about the three well-known measures of overlap, namely Matusita’s measure, Morisita’s measure and Weitzman’s measure for two exponential populations with different means. The asymptotic bias and variance of overlap measures estimators are derived. In small sample cases and due to the difficulty of calculating either the precision or the bias of the resulting estimators of overlap measures, Monte Carlo evaluations are used. Confidence intervals for those measures are also constructed via bootstrap method and Taylor approximation. A real data example is used to illustrate our proposed estimators.

Reducing Sample Size Needed for Accelerated Failure Time Model Using More Efficient Sampling Methods

Survival data are time-to-event data, such as time to death, time to appearance of a tumor, or time to recurrence of a disease. Accelerated failure time (AFT) models provide a linear relationship between the log of the failure time and covariates that affect the expected time to failure by contracting or expanding the time scale. The AFT model has intensive application in the field of social, medical, behavioral, and public health sciences. In this article we propose a more efficient sampling method of recruiting subjects for survival analysis. We propose using a Moving Extreme Ranked Set Sampling (MERSS) or an Extreme Ranked Set Sampling (ERSS) scheme with ranking based on an easy-to-evaluate baseline auxiliary variable known to be associated with survival time. This article demonstrates that these approaches provide a more powerful testing procedure, as well as a more efficient estimate of hazard ratio, than that based on simple random sampling (SRS). Theoretical derivation and simulation studies are provided. The Iowa 65+ Rural Health Study data are used to illustrate the methods developed in this article.

The Inverse Weibull Distribution as a Failure Model Under Various Loss Functions and Based on Progressive First-Failure Censored Data

Abstract In this article we consider statistical inferences about the unknown parameters of the inverse Weibull distribution based on progressively first-failure censoring using Bayesian procedures. The Bayes estimators are obtained based on both the symmetric and asymmetric (Linex, General Entropy and Precautionary) loss functions. There are no explicit forms for the Bayes estimators; therefore, we propose the Lindley’s approximation method to compute the Bayes estimators. A comparison between these estimators and the maximum likelihood estimator (MLE) is provided by using extensive simulation and two criteria, namely, the bias and the mean squared error. It is concluded that the approximate Bayes estimators outperform the MLEs most of the time. Real life data example is provided to illustrate our proposed estimators.