Minimum-Distance Parametric Estimation Under Progressive Type-I Censoring

Inferences of accelerated generalized type-I hybrid censoring data under power hazard rate population

Various types of failure, censored and accelerated life tests, are commonly employed for life testing in some manufacturing industries and products that are highly reliable. In this article, we consider the tampered failure rate model as one of such types that relate the distribution under use condition to the distribution under accelerated condition. It is assumed that the lifetimes of products under use condition have generalized Pareto distribution as a lifetime model. Some estimation methods such as graphical, moments, probability weighted moments, and maximum likelihood estimation methods for the parameters are discussed based on progressively type-I censored data. The determination of optimal stress change time is discussed under two different criteria of optimality. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

This paper discussed robust estimation for point estimation of the shape and scale parameters for generalized exponential (GE) distribution using a complete dataset in the presence of various percentages of outliers. In the case of outliers, it is known that classical methods such as maximum likelihood estimation (MLE), least square (LS) and maximum product spacing (MPS) in case of outliers cannot reach the best estimator. To confirm this fact, these classical methods were applied to the data of this study and compared with non-classical estimation methods. The non-classical (Robust) methods such as least absolute deviations (LAD), and M-estimation (using M. Huber (MH) weight and M. Bisquare (MB) weight) had been introduced to obtain the best estimation method for the parameters of the GE distribution. The comparison was done numerically by using the Monte Carlo simulation study. The two real datasets application confirmed that the M-estimation method is very much suitable for estimating the GE parameters. We concluded that the M-estimation method using Huber object function is a suitable estimation method in estimating the parameters of the GE distribution for a complete dataset in the presence of various percentages of outliers.

In this article, an attempt is made to propose a novel method of lifetime distributions with maximum flexibility using a popular T–X approach together with an exponential distribution, which is known as the New Generalized Logarithmic-X Family (NGLog–X for short) of distributions. Additionally, the generalized form of the Weibull distribution was derived by using the NGLog–X family, known as the New Generalized Logarithmic Weibull (NGLog–Weib) distribution. For the proposed method, some statistical properties, including the moments, moment generating function (MGF), residual and reverse residual life, identifiability, order statistics, and quantile functions, were derived. The estimation of the model parameters was derived by using the well-known method of maximum likelihood estimation (MLE). A comprehensive Monte Carlo simulation study (MCSS) was carried out to evaluate the performance of these estimators by computing the biases and mean square errors. Finally, the NGLog–Weib distribution was implemented on four real biomedical datasets and compared with some other distributions, such as the Alpha Power Transformed Weibull distribution, Marshal Olkin Weibull distribution, New Exponent Power Weibull distribution, Flexible Reduced Logarithmic Weibull distribution, and Kumaraswamy Weibull distribution. The analysis results demonstrate that the new proposed model performs as a better fit than the other competitive distributions.

This paper presents a new Marshall-Olkin extended family of distributions with bounded support. Some of the Mathematical properties of the proposed distribution were studied and the method of maximum likelihood estimation was employed to estimate the unknown parameters of the proposed distribution. A Monte Carlo simulation study was carried out to examine the asymptotic behaviour of the parameter estimates of the distribution.” Finally, two real data sets defined on a unit interval were used to show the applicability of the proposed distribution in analyzing real data sets.

In this paper, we propose a new flexible lifetime distribution. The proposed distribution will be referred to as beta power Muth distribution. It can be used to model increasing, decreasing, bathtub shaped or upside-down bathtub hazard rates. Some properties of the new model are obtained including moments, quantile function and moments of the order statistics. The unknown model parameters are estimated by the maximum likelihood method of estimation. A Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimates. Two reliability data sets are applied to illustrate the usefulness and flexibility of the proposed model. In addition, we introduce a new location-scale regression model based on the logarithm of the proposed distribution and provide a real data application.

This paper studies estimation of the parameters of the generalized Gompertz distribution based on ranked-set sample (RSS). Maximum likelihood (ML) and Bayesian approaches are considered. Approximate confidence intervals for the unknown parameters are constructed using both the normal approximation to the asymptotic distribution of the ML estimators and bootstrapping methods. Bayes estimates and credible intervals of the unknown parameters are obtained using differential evolution Markov chain Monte Carlo and Lindley’s methods. The proposed methods are compared via Monte Carlo simulations studies and an example employing real data. The performance of both ML and Bayes estimates is improved under RSS compared with simple random sample (SRS) regardless of the sample size. Bayes estimates outperform the ML estimates for small samples, while it is the other way around for moderate and large samples.

Location-scale models in the field of meta-analysis allow researchers to simultaneously study the influence of moderator variables on the mean (location) and variance (scale) of the distribution of true effects. However, the increased complexity of such models can make model fitting challenging. Moreover, the statistical properties of the estimation and inference methods for such models have not been systematically examined in the meta-analytic context. We therefore conducted a Monte Carlo simulation study to compare different estimation methods (maximum or restricted maximum likelihood estimation), significance tests (Wald-type, permutation, and likelihood-ratio tests), and methods for constructing confidence intervals (Wald-type and profile-likelihood intervals) for the scale coefficients of such models. When restricted maximum likelihood estimation was used, slightly closer to nominal rejection rates and narrower confidence intervals were obtained. The permutation test yielded type I error rates closest to the nominal level, whereas the likelihood-ratio test obtained the highest statistical power. In most scenarios, profile-likelihood intervals showed lower coverage probabilities than the Wald-type method but closer to the nominal 95% level. Finally, slightly higher rejection rates and coverage probabilities were obtained when a dichotomous moderator was examined rather than a continuous one. Despite the need to use some constraints on the parameter space for the scale coefficients and the possibility of non-convergence of some procedures that may affect the fitting of the specified models, location-scale models proved to be a valid and useful tool for modeling the heterogeneity parameter in meta-analysis.

Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have been proposed in the literature, most of them can be highly sensitive to the presence of a small proportion of atypical observations in the training set. A review of outlier robust estimation methods for nonparametric regression models is provided, paying particular attention to practical considerations. Since outliers can also influence negatively the regression estimator by affecting the selection of bandwidths or smoothing parameters, a discussion of robust alternatives for this task is also included. Using many of the “classical” nonparametric regression estimators (and their robust counterparts) can be very challenging in settings with a moderate or large number of explanatory variables, so recently proposed robust nonparametric regression methods that scale well with a growing number of covariates are also discussed.

Robust fitting of mixture regression models

Bell regression model has become a very versatile model that replaced the conventional count data models and helps to resolve the problem of over-dispersion where the variance of data points surpasses the mean. Nevertheless, in practice, the classical maximum likelihood estimators (MLE) of the parameters of a model are frequently affected by multicollinearity among the explanatory variables, and they yield highly unstable estimates and inflated variances. To address these difficulties, estimation methods developed to estimate shrinkage, such as ridge or Liu estimators have been applied to the Bell regression model. In the subject review, new developments in estimators of shrinkage of Bell regression models are proportionate in discussing their theoretical background in knowledge, estimation process, and asymptotic characteristics. The results on Monte Carlo simulation studies always show that shrinkage estimators outweigh MLEs in that they minimize mean squared error and bias more than MLEs, especially in cases of multicollinearity. Both overall, estimation methods of shrinkage is a considerable improvement in Bell regression modeling that offers certainty and effectiveness of analysis of complicated counts information utilizing problematic distribution attributes.

Analysis of jointly censoring schemes has received considerable attention in the last few years. In this paper, maximum likelihood and Bayes methods of estimation are used to estimate the unknown parameters of two Gompertz populations under a joint progressive Type-II censoring scheme. Bayesian estimations of the unknown parameters are obtained based on squared error loss functions under the assumption of independent gamma priors. We propose to apply the Markov Chain Monte Carlo technique to carry out a Bayes estimation procedure. The approximate, bootstrap, and credible confidence intervals for the unknown parameters are also obtained. Also, reliability and hazard rate function of the two Gompertz populations under joint progressive Type-II censoring scheme is obtained and the corresponding approximate confidence intervals. Finally, all the theoretical results obtained are assessed and compared using two real-world data sets and Monte Carlo simulation studies.

The probability P(Y < X) plays an important role in reliability analysis as it represents reliability in a stress–strength model and availability when Y and X are stress and strength variables, respectively. In reliability theory Lindley distribution has been established as a useful lifetime model and inference procedures for its reliability characteristics are being developed in the literature. To develop these inferences, life testing experiments are conducted which are time consuming and costly in nature. To save time and money various types of censoring plans are used. One such censoring scheme called Progressive censoring has recently become very popular in reliability theory. Progressively first failure censoring is a generalization of progressive censoring scheme and is useful in various practical situations when testing material is inexpensive. In view of above in this paper, maximum likelihood and Bayes estimates for the parameter δ = P(Y < X) are studied when X and Y are Lindley random variables. The data are collected using progressively first failure censoring. A Monte Carlo simulation study is performed to compare different methods of estimation. Two examples, including a real data example, are also given to illustrate the proposed estimates in the paper.

Estimation for the three-parameter gamma distribution based on progressively censored data

Quantile regression has become a standard modern econometric method because of its capability to investigate the relationship between economic variables at various quantiles. The econometric method of Markov-switching regression is also considered important because it can deal with structural models or time-varying parameter models flexibly. A combination of these two methods, known as “Markov-switching quantile regression (MSQR),” has recently been proposed. Liu and, Liu and Luger propose MSQR models using the Bayesian approach whereas Ye et al.’s proposal for MSQR models is based on the classical approach. In our study, we extend the results of Ye et al. First, we propose an efficient estimation method based on the expectation-maximization algorithm. In our second extension, we adopt the quasi-maximum likelihood approach to estimate the proposed MSQR models unlike the maximum likelihood approach that Ye et al. use. Our simulation results confirm that the proposed expectation-maximization (EM) estimation method for MSQR models works quite well.