Search Results (80)

The natural generalization of the XLindley distribution is proposed. The mathematical properties of the generalized XLindley distribution are derived. The importance of the proposed model is evaluated on the first-order autoregressive process, and compared with its counterparts. Extensive simulation studies are carried out to demonstrate the suitability of the estimation methods. Empirical findings reveal that the first-order autoregressive process with generalized XLindley innovations produces better forecasting results than those of the gamma, weighted Lindley, and normal innovations. Additionally, a web-tool application of the proposed model is developed and deployed on a free server that is accessible for practitioners. Full article

In this paper, the half-logistic generalized power Lindley distribution, a new two-parameter lifetime model for positive and heavy-tailed data, is proposed and studied. Several mathematical properties are derived, including closed-form expressions for the density, distribution, survival, hazard, and the Lambert W quantile function, as well as series expansions for moments, skewness, kurtosis, and Rényi entropy. Parameter estimation is performed using maximum likelihood and Bayesian methods, where Bayesian estimation is implemented via the Metropolis–Hastings algorithm. A Monte Carlo simulation study is conducted to evaluate the estimators’ performance, showing decreasing bias and mean squared error with larger samples. Finally, three real-world datasets are analyzed to demonstrate that the proposed distribution provides superior fit compared to Lindley-type competitors and the Weibull distribution, based on likelihood values, information criteria, and empirical diagnostics. Full article

In this work, we present a robust examination of the Bayesian estimators utilizing the two-parameter Upper truncated XLindley model, a unique Lindley model variant, and the oscillation of posterior risks. We provide the model in a censored scheme along with its likelihood function. The topic of sensitivity and robustness analysis of the Bayesian estimators was only covered by a small number of authors. As a result, very few apps have been created in this field. The oscillation of the posterior hazards of the Bayesian estimator is used to illustrate the method. By using a Monte Carlo simulation study, we show that, with the correct generalized loss function, a robust Bayesian estimator of the parameters corresponding to the smallest oscillation of the posterior risks may be obtained; robust estimators can be obtained when the parameter space is low-dimensional. The robustness and precision of Bayesian parameter estimation can be enhanced in regimes where the parameters of interest are of small magnitude. Full article

Modern healthcare and engineering both rely on robust reliability models, where handling censored data effectively translates into longer-lasting devices, improved therapies, and safer environments for society. To address this, we develop a novel inferential framework for the ZLindley (ZL) distribution under the improved adaptive progressive Type-II censoring strategy. The proposed approach unifies the flexibility of the ZL model—capable of representing monotonically increasing hazards—with the efficiency of an adaptive censoring strategy that guarantees experiment termination within pre-specified limits. Both classical and Bayesian methodologies are investigated: Maximum likelihood and log-transformed likelihood estimators are derived alongside their asymptotic confidence intervals, while Bayesian estimation is conducted via gamma priors and Markov chain Monte Carlo methods, yielding Bayes point estimates, credible intervals, and highest posterior density regions. Extensive Monte Carlo simulations are employed to evaluate estimator performance in terms of bias, efficiency, coverage probability, and interval length across diverse censoring designs. Results demonstrate the superiority of Bayesian inference, particularly under informative priors, and highlight the robustness of HPD intervals over traditional asymptotic approaches. To emphasize practical utility, the methodology is applied to real-world reliability datasets from clinical trials on leukemia patients and hydrological measurements from River Styx floods, demonstrating the model’s ability to capture heterogeneity, over-dispersion, and increasing risk profiles. The empirical investigations reveal that the ZLindley distribution consistently provides a better fit than well-known competitors—including Lindley, Weibull, and Gamma models—when applied to real-world case studies from clinical leukemia trials and hydrological systems, highlighting its unmatched flexibility, robustness, and predictive utility for practical reliability modeling. Full article

This paper introduces the Lambert-Lindley distribution, a two-parameter extension of the Lindley model constructed through the Lambert-F generator. The new distribution retains the non-negative support of the Lindley distribution and provides additional flexibility by incorporating a shape parameter that controls skewness and tail behavior. Structural properties are derived, including the probability density function, cumulative distribution function, quantile function, hazard rate, and moments. Parameter estimation is addressed using the method of moments and maximum likelihood, and a Monte Carlo simulation study carried out to evaluate the performance of the proposed estimators. The practical applicability of the Lambert–Lindley distribution is demonstrated with two real datasets: stress rupture times of Kevlar/epoxy composites and hospital stay durations of breast cancer patients. Comparative analyses using goodness-of-fit tests and information criteria demonstrate that the proposed model can outperform classical alternatives such as the Gamma and Weibull distributions. Consequently, the Lambert–Lindley distribution emerges as a flexible alternative for modeling positive unimodal data in contexts such as material reliability studies and clinical duration analysis. Full article

In this paper, the ranked set sampling method (RSS) is considered for estimating the inverse power Lindley distribution (IPLD) parameters and compared with the commonly simple random sampling. Different estimation methods are investigated including the commonly maximum likelihood, minimum distance estimation methods (Anderson Darling (AD), right tail Anderson Darling, left tail Anderson Darling, AD left tail second order, Cramér-von Mises), methods of maximum and minimum spacing distance (maximum product spacing distance, minimum spacing distance), methods of ordinary and weighted least squares, and the Kolmogorov–Smirnov method. A simulation study is conducted to compare these methods using RSS and SRS based on the same number of measured units in terms of mean squared error, bias, efficiency, and mean relative estimation error. A failure data set is fitted to the IPLD and the proposed estimation methods are applied to the data. Full article

This paper presents a comprehensive study on the estimation of multicomponent stress–strength reliability under progressively censored data, assuming the inverse Rayleigh distribution. Both maximum likelihood estimation and Bayesian estimation methods are considered. The loss function and prior distribution play crucial roles in Bayesian inference. Therefore, Bayes estimators of the unknown model parameters are obtained under symmetric (squared error loss function) and asymmetric (linear exponential and general entropy) loss functions using gamma priors. Lindley and MCMC approximation methods are used for Bayesian calculations. Additionally, asymptotic confidence intervals based on maximum likelihood estimators and Bayesian credible intervals constructed via Markov Chain Monte Carlo methods are presented. An extensive Monte Carlo simulation study compares the efficiencies of classical and Bayesian estimators, revealing that Bayesian estimators outperform classical ones. Finally, a real-life data example is provided to illustrate the practical applicability of the proposed methods. Full article

In this article, we propose a goodness-of-fit test for a one-parameter Lindley distribution based on energy statistics. The Lindley distribution has been widely used in reliability studies and survival analysis, especially in applied sciences. The proposed test procedure is simple and more powerful against general alternatives. Under different settings, Monte Carlo simulations show that the proposed test is able to be well controlled for any given nominal levels. In terms of power, the proposed test outperforms other existing similar methods in different settings. We then apply the proposed test to real-life datasets to demonstrate its competitiveness and usefulness. Full article

In this paper, we address the problem of increasing the number of regenerations in the simulation of the workload process in a single-server queueing system. To this end, we extend the splitting technique developed for the Markov workload process in the M/M/1 queue to the more general GI/M/1 queueing systems. This approach is based on a minorization condition for the transition kernel of the workload process, which is a Markov chain defined by the Lindley recursion. The proposed method increases the number of regenerations during the simulation and potentially reduces the time required to estimate stationary performance metrics with a given level of precision. Full article

In this paper, a size-biased Lindley (SBL) first-order autoregressive (AR(1)) process is proposed, the so-called SBL-AR(1). Some probabilistic and statistical properties of the proposed process are determined, including the distribution of its innovation process, the Laplace transformation function, multi-step-ahead conditional measures, autocorrelation, and spectral density function. In addition, the unknown parameters of the model are estimated via the conditional least squares and Gaussian estimation methods. The performance and behavior of the estimators are checked through some numerical results by a Monte Carlo simulation study. Additionally, two real-world datasets are utilized to examine the model’s applicability, and goodness-of-fit statistics are used to compare it to several pertinent non-Gaussian AR(1) models. The findings reveal that the proposed SBL-AR(1) model exhibits key theoretical properties, including a closed-form innovation distribution, multi-step conditional measures, and an exponentially decaying autocorrelation structure. Parameter estimation via conditional least squares and Gaussian methods demonstrates consistency and efficiency in simulations. Real-world applications to inflation expectations and water quality data reveal a superior fit over competing non-Gaussian AR(1) models, evidenced by lower values of the AIC and BIC statistics. Forecasting comparisons show that the classical conditional expectation method achieves accuracy comparable to some modern machine learning techniques, underscoring its practical utility for skewed and fat-tailed time series. Full article

This paper investigates various estimation methods for the parameters of the unit Lindley distribution (U-LD) under both ranked set sampling (RSS) and simple random sampling (SRS) designs. The distribution parameters are estimated using the maximum likelihood estimation, ordinary least squares, weighted least squares, maximum product of spacings, minimum spacing absolute distance, minimum spacing absolute log-distance, minimum spacing square distance, minimum spacing square log-distance, linear-exponential, Anderson–Darling (AD), right-tail AD, left-tail AD, left-tail second-order, Cramér–von Mises, and Kolmogorov–Smirnov. A comprehensive simulation study is conducted to assess the performance of these estimators, ensuring an equal number of measuring units across both designs. Additionally, two real datasets of items failure time and COVID-19 are analyzed to illustrate the practical applicability of the proposed estimation methods. The findings reveal that RSS-based estimators consistently outperform their SRS counterparts in terms of mean squared error, bias, and efficiency across all estimation techniques considered. These results highlight the advantages of using RSS in parameter estimation for the U-LD distribution, making it a preferable choice for improved statistical inference. Full article

We consider a Lindley process with Laplace-distributed space increments. We obtain closed-form recursive expressions for the density function of the position of the process and for its first exit time distribution from the domain $[0,h]$. We illustrate the results in terms of the parameters of the process. An example of the application of the analytical results is discussed in the framework of the CUSUM method. Full article

This paper presents a new bivariate mixture Lindley power function (BMLPF) distribution that employs a conditional approach with non-identical asymmetric distributions, distinguishing itself by the incorporation of a functional shape parameter. Various structural properties of bivariate distribution are presented, including explicit marginals, cumulative distribution function (CDF), product moments, correlation coefficients, conditional densities, moment generating functions, conditional mean, and variances. The parameters of the proposed distribution are evaluated using the maximum likelihood estimation method. To assess the effectiveness of this estimation approach, an extensive simulation study is carried out. The analysis quantifies these point estimators with their standard errors, RMSE, LCL, and UCL. This research significantly contributes to the development and application of bivariate distributions particularly in modeling and analyzing various types of data. Full article

In this manuscript, a new two-parameter stochastic distribution is proposed and obtained by a continuous half-logistic transformation of the quasi-Lindley (QL) distribution to the unit interval. The resulting distribution, named the quasi-Lindley half-logistic unit (QHU) distribution, is examined in terms of its key stochastic properties, such as asymmetry conditions, shape and modality, moments, etc. In addition, the stochastic dominance of the proposed distribution with respect to its parameters is considered, and it is shown that the QHU distribution, in contrast to the QL distribution that is always positively asymmetric, can have both asymmetric forms. The parameters of the QHU distribution are estimated by the maximum likelihood (ML) method, and the asymptotic properties of thusly obtained estimators are examined. Finally, an application of the proposed distribution in modeling some real-world phenomena is also presented. Full article

The Bivariate Odd Lindley Half-Logistic (BOLiHL) distribution with progressive Type-II censoring provides a powerful statistical tool for analyzing dependent data effectively. This approach benefits society by enhancing engineering systems, improving healthcare decisions, and supporting effective risk management, all while optimizing resources and minimizing experimental burdens. In this paper, the likelihood function derived under progressive Type-II censoring is generalized for the BOLiHL distribution. The well-known maximum likelihood estimation method and Bayesian estimation are applied to evaluate the parameters of the distribution. A study utilizing simulation techniques is performed to evaluate the performance of the estimators, using statistical analysis metrics for censored observations under a progressive Type-II censoring scheme with varying sample sizes, failure times, and censoring schemes. Additionally, a real dataset is studied to validate the proposed model, delivering impactful analyses for practical applications. Full article