计量经济分析 = Econometric analysis

In this paper, we discuss different predictors of times to failure of units censored in multiple stages in a progressively censored sample from Pareto distribution. The best linear unbiased predictors, maximum likelihood predictors and approximate maximum likelihood predictors are considered. We also present two methods for obtaining prediction intervals for the times to failure of units. A numerical simulation study involving two data sets is presented to illustrate the methods of prediction.

Prediction for Pareto distribution based on progressively type II censored samples

This paper aims to model the COVID-19 mortality rates in Italy, Mexico, and the Netherlands, by specifying an optimal statistical model to analyze the mortality rate of COVID-19. A new lifetime distribution with three-parameter is introduced by a combination of Rayleigh distribution and extended odd Weibull family to produce the extended odd Weibull Rayleigh (EOWR) distribution. This new distribution has many excellent properties as simple linear representation, hazard rate function, and moment generating function. Maximum likelihood, maximum product spacing and Bayesian estimation methods are applied to estimate the unknown parameters of EOWR distribution. MCMC method is used for the Bayesian estimation. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. Also, data analysis for the real data of mortality rate is considered.

A New Extended Rayleigh Distribution with Applications of COVID-19 Data.

This paper introduces the new novel four-parameter Weibull distribution named as the Marshall–Olkin alpha power Weibull (MOAPW) distribution. Some statistical properties of the distribution are examined. Based on Type-I censored and Type-II censored samples, maximum likelihood estimation (MLE), maximum product spacing (MPS), and Bayesian estimation for the MOAPW distribution parameters are discussed. Numerical analysis using real data sets and Monte Carlo simulation are accomplished to compare various estimation methods. This novel model’s supremacy upon some famous distributions is explained using two real data sets and it is shown that the MOAPW model can achieve better fits than other competitive distributions.

/pdf/marshall-olkin-alpha-power-weibull-distribution-different-1t11owlkht.pdf

Marshall–Olkin Alpha Power Weibull Distribution: Different Methods of Estimation Based on Type-I and Type-II Censoring

This paper is concerned with statistical inference of multiple constant-stress testing for progressive type-II censored data with binomial removal. The failure times of the test units are assumed to be independent and follow the modified Kies exponential (MKEx) distribution. The maximum likelihood method as well as Bayes method are used to derive both point and interval estimates of the parameters. Furthermore, a real data application for transformers turn insulation is used to illustrate the proposed methods. Moreover, this real data set is used to show that MKEx distribution can be a possible alternative model to the exponential, generalized exponential and Weibull distributions. Finally, simulation studies are carried out to investigate the accuracy of the different estimation methods.

Accelerated life tests for modified Kies exponential lifetime distribution: binomial removal, transformers turn insulation application and numerical results

In this article, the statistical inference for the Gompertz distribution based on Type-II progressively hybrid censored data is discussed. The estimation of the parameters for Gompertz distribution is obtained using maximum likelihood method (MLE) and Bayesian method under three different loss functions. We also proved the existence and uniqueness of the MLE. The one-sample Bayesian prediction intervals are obtained. The work is done for different values of the parameters. We apply the Monto Carlo simulation to compare the proposed methods, also an example is discussed to construct the Prediction intervals.

Statistical inference for the Gompertz distribution based on Type-II progressively hybrid censored data

In this paper, the statistical inference for the Gompertz distribution based on generalized progressively hybrid censored data is discussed. The estimation of the parameters for Gompertz distribution is discussed using the maximum likelihood method and the Bayesian methods under different loss functions. The existence and uniqueness of the maximum likelihood estimation are proved. The point and interval Bayesian predictions for unobserved failures from the same sample and that from the future sample are derived. The Monte Carlo simulation is applied to compare the proposed methods. A real data example is used to apply the methods of estimation and to construct the prediction intervals.

Estimation and Prediction for Gompertz Distribution Under the Generalized Progressive Hybrid Censored Data

In this paper, we use the generalized progressive hybrid censoring sample from the Burr Type-Ⅻ distribution to estimate the unknown parameters, reliability and hazard functions. We apply the maximum likelihood (ML) and the Bayesian estimation under different prior distributions and different loss functions; namely; are the squared error, Linex and general entropy. Also, we construct the classical and credible intervals of the unknown parameters as well as for the survival and hazard functions. In addition, we investigate the performance of the point estimation by using the mean square error (MSE) and expected bias (EB) and performance of the interval estimation using the average length and coverage probability. Further, we develop the Bayesian one- and two- samples Bayesan prediction for the non-observed failures in the progressive censoring. In order to show the performance and usefulness of the inferential procedures, we carry out some simulation experiments using MCMC Algorithm for the Bayesian approach based on different prior distributions. Finally, we apply the theatrical finding to some real life data set.

Analysis of the generalized progressive hybrid censoring from Burr Type-XII lifetime model

In reliability studies, the best fitting of lifetime models leads to accurate estimates and predictions, especially when these models have nonmonotone hazard functions. For this purpose, the new Exponential-X Frechet (NEXF) distribution that belongs to the new exponential-X (NEX) family of distributions is proposed to be a superior fitting model for some reliability models with nonmonotone hazard functions and beat the competitive distribution such as the exponential distribution and Frechet distribution with two and three parameters. So, we concentrated our effort to introduce a new novel model. Throughout this research, we have studied the properties of its statistical measures of the NEXF distribution. The process of parameter estimation has been studied under a complete sample and Type-I censoring scheme. The numerical simulation is detailed to asses the proposed techniques of estimation. Finally, a Type-I censoring real-life application on leukaemia patient's survival with a new treatment has been studied to illustrate the estimation methods, which are well fitted by the NEXF distribution among all its competitors. We used for the fitting test the novel modified Kolmogorov-Smirnov (KS) algorithm for fitting Type-I censored data.

/pdf/statistical-inference-under-censored-data-for-the-new-40mrnbf67y.pdf

Statistical Inference under Censored Data for the New Exponential-X Fréchet Distribution: Simulation and Application to Leukemia Data.

In this article, a progressive-stress accelerated life test (ALT) that is based on progressive type-II censoring is studied. The cumulative exposure model is used when the lifetime of test units follows Pareto-IV distribution. Different estimates as the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) for the model parameters are discussed. Bayesian estimates are derived while using the Tierney and Kadane (TK) approximation method and the importance sampling method. The asymptotic and bootstrap confidence intervals (CIs) of the parameters are constructed. A real data set is analyzed in order to clarify the methods proposed through this paper. Two types of the progressive-stress tests, the simple ramp-stress test and multiple ramp-stress test, are compared through the simulation study. Finally, some interesting conclusions are drawn.

https://www.mdpi.com/2227-7390/8/10/1786/pdf

M. H. Abu-Moussa

Papers

Statistical inference for the Gompertz distribution based on Type-II progressively hybrid censored data

Estimation and Prediction for Gompertz Distribution Under the Generalized Progressive Hybrid Censored Data

Analysis of the generalized progressive hybrid censoring from Burr Type-XII lifetime model

Statistical Inference under Censored Data for the New Exponential-X Fréchet Distribution: Simulation and Application to Leukemia Data.

Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study