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The Lomax distribution is one of the well-known distributions that is used to fit heavy-tailed data. In this paper, we investigate the estimation of Shannon entropy of the Lomax distribution using noninformative priors. Some important priors including Jeffreys prior, reference priors and probability matching priors are presented. We demonstrate that the reference and matching priors for the Lomax entropy do not match the reference and probability matching priors of the Lomax parameters, regardless of which parameter of interest is considered. The propriety and the existence of the expectation of the posterior under each prior are validated, respectively. A simulation study is conducted to assess the frequentist performance of the proposed Bayesian estimates in terms of the mean squared error and coverage probability. Finally, the approach is applied to three real data sets for illustrative purposes. [ABSTRACT FROM AUTHOR]

Mixture models are more appealing and appropriate for studying the heterogeneous nature of lifetimes of certain mechanical, biological, social, economic and several other processes as compared to simple models. This paper considers a mixture of generalized Rayleigh distributions under classical and Bayesian perspectives based on type I censored samples. The new distribution which exhibits decreasing, decreasing-increasing-decreasing, unimodal and bimodal shaped density while the distribution has the ability to model lifetime data with increasing, increasing-decreasing-increasing, bathtub and bi-bathtub-shaped failure rates. We derive some basic and structural properties of the proposed distribution. Moreover, we estimate the parameters of the model by using frequentist and Bayesian approaches. In frequentist method, the maximum likelihood estimate of the parameters and their asymptotic confidence intervals are obtained while for Bayesian analysis, the squared error loss (SEL) function and uniform as well as beta and gamma priors are considered to obtain the Bayes estimators of the unknown parameters of the model. Furthermore, the highest posterior density (HPD) credible intervals are also obtained. In real data analysis, in addition to point estimates of the model parameters, asymptotic confidence intervals and HPD credible intervals, two bootstrap CIs are also provided. Monte Carlo simulation study is performed to assess the behavior of these estimators. An application of the model is presented by re-analyzing strength for single carbon fibers data set. [ABSTRACT FROM AUTHOR]

This paper introduces a new class of distributions by compounding the inverse Lindley distribution and power series distributions which is called compound inverse Lindley power series (CILPS) distributions. An important feature of this distribution is that the lifetime of the component associated with a particular risk is not observable, rather only the minimum lifetime value among all risks is observable. Further, these distributions exhibit an unimodal failure rate. Various properties of the distribution are derived. Besides, two special models of the new family are investigated. The model parameters of the two sub-models of the new family are obtained by the methods of maximum likelihood, least square, weighted least square and maximum product of spacing and compared them using the Monte Carlo simulation study. Besides, the log compound inverse Lindley regression model for censored data is proposed. Three real data sets are analyzed to illustrate the flexibility and importance of the proposed models. [ABSTRACT FROM AUTHOR]

We consider the generalized extended exponential-Weibull distribution, which can be very useful for modelling non-monotonic failure rate function, and provide a detailed study of its structural properties. This model includes at least thirteen sub-models and some of them are very known such as the Weibull, generalized Weibull, exponential-Weibull, and exponentiated generalized linear exponential distributions. We also consider different estimation procedures for estimating the model parameters, namely: maximum likelihood, least-square, weighted least-square, maximum product of spacings, Cramér-von-Mises, and Anderson-Darling methods. We also conduct Monte Carlo simulation experiments to assess the finite sample properties of the proposed estimation methods. The usefulness of the distribution is illustrated by means of two real data sets to prove its versatility in practical applications. [ABSTRACT FROM AUTHOR]

We take an in-depth look at the weighted Burr-XII distribution. This distribution generalizes Burr-XII, Lomax, and log-logistic distributions. We discuss the distributional characteristics of the probability density function, the failure rate function, and mean residual lifetime of this distribution. Moreover, we obtain various statistical properties of this distribution such as moment generating function, entropies, mean deviations, order statistics and stochastic ordering. The estimation of the distribution parameters via maximum likelihood method and the observed Fisher information matrix are discussed. We further employ a simulation study to investigate the behav- ior of the maximum likelihood estimates (MLEs). A test concerning the existence of size-bias in the sample is provided. In the end, a real data is presented and it is analyzed using this distribution along with some existing distributions for illustrative purposes. [ABSTRACT FROM AUTHOR]

This paper addresses the estimation of the unknown parameters of the alpha power exponential distribution (Mahdavi and Kundu, 2017) using nine frequentist estimation methods. We discuss the finite sample properties of the parameter estimates of the alpha power exponential distribution via Monte Carlo simulations. The potentiality of the distribution is analyzed by means of two real data sets from the fields of engineering and medicine. Finally, we use the maximum likelihood method to derive the estimates of the distribution parameters under competing risks data and analyze one real data set. [ABSTRACT FROM AUTHOR]

In this paper, a new sampling technique is proposed that carries more information than contained in ranked set sample (RSS). The proposed sampling technique is defined by making the use for the idea of visual grouping of population units with respect to a fixed threshold and RSS. We refer to it as RSS-Grouping technique. Under the best informative RSS-Grouping technique, the maximum likelihood estimator (MLE) of the mean of an exponential distribution is derived. This MLE is then compared to various candidate estimators through extensive simulation experiments. Numerical results show that the MLE under the best informative RSS-Grouping scheme is preformed better than these estimators. The effects of imperfect sampling on the behavior of the MLE under the proposed scheme is also studied. We conduct a simulation study to assess the finite sample behavior of the MLE under imperfect sampling and imperfect classification of visual grouping. Similarly, the simulation study shows that the MLE is behaved asymptotically unbiased. Additionally, the MLE tends to be at least as efficient as the MLE under RSS regardless of raking errors and the estimation of the threshold has slightly effects on the sampling distribution of the MLE. [ABSTRACT FROM AUTHOR]

In this article, a new three-parameter extension of the two-parameter log-logistic distribution is introduced. Several distributional properties such as moment-generating function, quantile function, mean residual lifetime, the Renyi and Shanon entropies, and order statistics are considered. The estimation of the model parameters for complete and right-censored cases is investigated competently by maximum likelihood estimation (MLE). A simulation study is conducted to show that these MLEs are consistent in moderate samples. Two real datasets are considered; one is a right-censored data to show that the proposed model has a superior performance over several existing popular models. [ABSTRACT FROM AUTHOR]