Exponentiated generalized linear exponential distribution

In this paper, recurrence relations for single and product moments of generalized order statistics (gOSs) from linear exponential distribution (LE) are derived and characterizations of this distribution based on the conditional moments of the gOSs are given.

In this paper, an extension of the linear failure rate distribution is proposed, called the weighted linear failure rate distribution. This class is a generalization of the two-parameter linear failure rate distribution as well as some other lifetime distributions. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. Different properties of this new distribution and the inference of the old parameters are discussed, the skewness parameter is examined, and some well-known lifetime distributions are introduced as special sub models. Finally, an application using various types of data is presented to demonstrate the flexibility of this distribution and for illustrative purposes.

For the first time, a five-parameter distribution, called the kumaraswamy quadratic hazard rate distribution is defined and studied. The new distribution contains as special models some well-known distributions discussed in lifetime literature, such as the Linear failure rate, Exponential and Rayleigh distributions, among several others. We obtain the moments, moment generating and quantile functions. We discuss the method of maximum likelihood to estimate the model parameters and determine the observed information matrix. A real data sets illustrate the importance and flexibility of the proposed models. Normal 0 false false false EN-US X-NONE AR-SA

A new family of Marshall–Olkin extended generalized linear exponential distribution

This paper introduces a new comprehensive four-parameter distribution called the modified generalized linear failure rate (MGLFR) distribution. The method generalizes some well-known and most commonly used distributions in reliability such as exponential, Rayleigh, linear failure rate, generalized linear failure rate and modified Weibull distribution. The study also investigates some essential properties of this new distribution and considers the problem of the evaluation of system reliability by describing the lifetimes of components based on a fuzzy MGLFR distribution and by developing fuzzy reliability characteristics. The results can be applied to determine the reliability of real objects where parameters of lifetime variable are subject to uncertainty.

This paper concerns with various techniques for estimations from the generalized linear exponential distribution (GLED) that can be used for modeling bathtub, increasing and decreasing hazard rate (HR) behavior and was first proposed by [3]. This distribution is important since it contains as special sub-models some widely well-known distributions such as the exponential distribution (ED), the Rayleigh distribution (RD), the linear exponential distribution (LED), and the Weibull distribution (WD). The various techniques for estimations can be considered as maximum likelihood estimation (MLE), least-square estimation (LSE), weighted least square estimation (WLSE), Cramer Von-Mises estimation (CVME), and Anderson Darling estimation (ADE). These methods of estimations are used to estimate the unknown parameters of the well-known GLED. Two applications are used to show that the GLED is a viable distribution in modeling lifetime data and to compare the varying methods of estimations based on the Kolmogorov-Simnorov test with the corresponding P-value to show the optimal method. Finally, a simulation study is presented to compare the varying methods of estimation based on the mean square error (MSE) and the average absolute bias (AAB).

A new exponentiated generalized linear exponential distribution (NEGLED) is introduced, which poses increasing, decreasing, bathtub-shaped, and constant hazard rate. Its various mathematical properties such as moments, quantiles, order statistics, hazard rate function (HRF), stress–strength parameter, etc. are derived. Five distributions, exponential distribution (ED), generalized linear exponential distribution (GLED), Rayleigh distribution (RD), Weibull distribution (WD), and generalized linear failure rate distribution (GLFRD) were used for comparison with NEGLED model using a dataset of blood cancer patients. Estimation of the parameters using the maximum likelihood estimation (MLE) method was obtained and to evaluate their performance a simulation study has been carried out. Finally, a dataset of 40 Leukemia patients was analysed for illustrative purpose proving that the NEGLED outperforms compared distributions.

Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.

The aim of this expository paper is to present the properties of the linear skew-t distribution, which is a specific example of a symmetry modulated-distribution. The skewing function remains the distribution function of Student’s t, but its argument is simpler than that used for the standard skew-t. The linear skew-t offers different insights, for example, different moments and tail behavior, and can be simpler to use for empirical work. It is shown that the distribution may be expressed as a hidden truncation model. The paper describes an extended version of the distribution that is analogous to the extended skew-t. For certain parameter values, the distribution is bimodal. The paper presents expressions for the moments of the distribution and shows that numerical integration methods are required. A multivariate version of the distribution is described. The bivariate version of the distribution may also be bimodal. The distribution is not closed under marginalization, and stochastic ordering is not satisfied. The properties of the distribution are illustrated with numerous examples of the density functions, table of moments and critical values. The results in this paper suggest that the linear skew-t may be useful for some applications, but that it should be used with care for methodological work.

We introduce in this paper a new six-parameters generalized version of the generalized linear failure rate (GLFR) distribution which is called McDonald Generalized Linear failure rate (McGLFR) distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a constant, decreasing, increasing, and upside down bathtub-and bathtub shaped failure rate function depending on its parameters. It includes some well-known lifetime distributions as special sub-models. Some structural properties of the new distribution are studied. Moreover we discuss maximum likelihood estimation of the unknown parameters of the new model.

The quality performance of many vital systems depends on how long the units are performing; hence, research works started focusing on increasing the reliability of systems while taking into consideration that many factors may cause the failures of operating systems. In this study, the combination of a parametric generalized linear failure rate distribution model and an adaptive progressive Type-II censoring scheme for practical purposes is explored. A comprehensive investigation is performed on the risk factors that cause failure and determines which of the factors has a more harmful effect on the units. A lifetime experiment is performed under the condition of an adaptive progressive Type-II censoring scheme to obtain observations as a result of the competing factors of failures. The obtained observations are assumed to follow a three-parameter generalized linear failure rate distribution and are assumed to be competing to cause failure. Two statistical inference methods are employed for estimating this model’s parameters: the frequentist maximum likelihood method and the Bayesian approach. Our model’s validity is demonstrated through extensive simulations and real data applications in the medical and electrical engineering fields.

This paper addresses the problems of frequentist and Bayesian estimation for the unknown parameters of generalized Lindley distribution based on lower record values. We first derive the exact explicit expressions for the single and product moments of lower record values, and then use these results to compute the means, variances and covariance between two lower record values. We next obtain the maximum likelihood estimators and associated asymptotic confidence intervals. Furthermore, we obtain Bayes estimators under the assumption of gamma priors on both the shape and the scale parameters of the generalized Lindley distribution, and associated the highest posterior density interval estimates. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential (LINEX)) loss functions. Finally, we compute Bayesian predictive estimates and predictive interval estimates for the future record values. To illustrate the findings, one real data set is analyzed, and Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation and prediction.

This article proposes a new family of continuous distributions generated from a log dagum random variable (named Log-Dagum Weibull Distribution) on the basis of T-X family technique. mathematical and statistical properties including survival function, hazard and reverse hazard function, Rth moments, L-moments, incomplete rth moments, quantile points, Order Statistics, Bonferroni and Lorenz curves as well as entropy measures for this class of distributions are presented also LDW distribution characterized by truncated moments order statistics and upper record values. Simulation study of the proposed family of distribution has been derived. The model parameters are obtained by the method of maximum likelihood estimation. We illustrate the performance of the proposed new family of distributions by means of four real data sets and the data sets show the new family of distributions is more appropriate as compared to Exponentiated exponential distribution (EED), Weibull distribution (WD), Gamma distribution (GD), NEED Nadarajah Exponentiated exponential distribution and Lomax distribution (LD). Moreover, perfection of competing models is also tested via the Kolmogrov-Simnorov (K S), the Anderson Darling (A*) and the Cramer-von Misses (W*). The measures of goodness of fit including the Akaike information criterion (AIC), consistent Akaike information criterion (CAIC), Bayesian information criterion (BIC), Hannan-Quinn information criterion (HQIC) are computed to compare the fitted models.

ABSTRACTIn a load-sharing system, the failure of a component affects the residual lifetime of the surviving components. We propose a model for the load-sharing phenomenon in k-out-of-m systems. The model is based on exponentiated conditional distributions of the order statistics formed by the failure times of the components. For an illustration, we consider two component parallel systems with the initial lifetimes of the components having Weibull and linear failure rate distributions. We analyze one data set to show that the proposed model may be a better fit than the model based on sequential order statistics.

This study aims to predict failure times for some units in some lifetime experiments. In some practical situations, the experimenter may not be able to register the failure times of all units during the experiment. Recently, this situation can be described by a new type of censored data called multiply-hybrid censored data. In this paper, the linear failure rate distribution is well-fitted to some real-life data and hence some statistical inference approaches are applied to estimate the distribution parameters. A two-sample prediction approach applied to extrapolate a new sample simulates the observed data for predicting the failure times for the unobserved units.