Search Results (112)

We introduce the discrete asymmetric double Lindley distribution, a new two-parameter family on the integer line designed to model signed counts and net changes with flexible asymmetric tail behavior. This statistical model is obtained by merging two Lindley-type linear-geometric kernels on the negative and non-negative half-lines, with tail decay rates that are coupled through a simple two-parameter mechanism. This construction yields an analytically tractable probability mass function with an explicit normalizing constant, as well as closed-form expressions for the cumulative distribution function and one-sided tail probabilities. We further provide a transparent stochastic representation based solely on Bernoulli and geometric random variables, leading to an exact and efficient simulation algorithm that is convenient for Monte Carlo studies and validating numerical likelihood routines. Graphical illustrations highlight the role of the asymmetry parameter in controlling the imbalance between the two tails and the resulting skewness on $\mathbb{Z}$. The proposed family offers a practical and interpretable alternative to existing integer-line models for asymmetric discrete data, with direct applicability to likelihood-based inference and real-world datasets. Full article

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

The New Polynomial Exponential Distribution (NPED), introduced by Beghriche et al. (2022), provides a flexible one-parameter family capable of representing diverse hazard shapes and heavy-tailed behavior. Regression frameworks based on the NPED, however, have not yet been established. This paper introduces two methodological extensions: (i) a generalized linear model (NPED-GLM) in which the distribution parameter depends on covariates, and (ii) a Poisson–NPED count regression model suitable for overdispersed and heavy-tailed count data. Likelihood-based inference, asymptotic properties, and simulation studies are developed to investigate the performance of the estimators. Applications to engineering failure-count data and insurance claim frequencies illustrate the advantages of the proposed models relative to classical Poisson, negative binomial, and Poisson–Lindley regressions. These developments substantially broaden the applicability of the NPED in actuarial science, reliability engineering, and applied statistics. Full article

This paper introduces a novel extension of the classical Lindley distribution, termed the X-Lindley model, obtained by a specific mixture of exponential and Lindley distributions, thereby substantially enriching the distributional flexibility. To enhance its inferential scope, a comprehensive reliability analysis is developed under a generalized progressive hybrid censoring scheme, which unifies and extends several traditional censoring mechanisms and allows practitioners to accommodate stringent experimental and cost constraints commonly encountered in reliability and life-testing studies. Within this unified censoring framework, likelihood-based estimation procedures for the model parameters and key reliability characteristics are derived. Fisher information is obtained, enabling the establishment of asymptotic properties of the frequentist estimators, including consistency and normality. A Bayesian inferential paradigm using Markov chain Monte Carlo techniques is proposed by assigning a conjugate gamma prior to the model parameter under the squared error loss, yielding point estimates, highest posterior density credible intervals, and posterior reliability summaries with enhanced interpretability. Extensive Monte Carlo simulations, conducted under a broad range of censoring configurations and assessed using four precision-based performance criteria, demonstrate the stability and efficiency of the proposed estimators. The results reveal low bias, reduced mean squared error, and shorter interval lengths for the XLindley parameter estimates, while maintaining accurate coverage probabilities. The practical relevance of the proposed methodology is further illustrated through two real-life data applications from engineering and physical sciences, where the XLindley model provides a markedly improved fit and more realistic reliability assessment. By integrating an innovative lifetime model with a highly flexible censoring strategy and a dual frequentist–Bayesian inferential framework, this study offers a substantive contribution to modern survival theory. 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

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

The genus Eryngium (Apiaceae Lindley) includes over 250 species distributed worldwide. In Michoacán, Mexico, 22 species have been recorded, among them E. beecheyanum (EB), E. heterophyllum (EH), and E. mexiae (EM), which are commonly used in traditional medicine. However, our understanding of their biology and chemical composition remains limited. This study evaluated the phytochemical profile, as well as the antioxidant and hypoglycemic activities of leaves and roots from these three wild species. Flavonoids, phenolic compounds, and sterols were analyzed using high-performance thin-layer chromatography (HPTLC). Antioxidant activity was assessed in vitro using ABTS·+ and DPPH· assays, while antihyperglycemic activity was determined by α-glucosidase inhibition. Six metabolites were detected across all species, with organ-dependent variation. In the leaves, EB showed a high rutin content (241.3 µg/mL), EM contained catechin (137.3 µg/mL), and EH exhibited β sitosterol (315.9 µg/mL). Both leaves and roots of all species showed notable antioxidant activity. EB leaves exhibited inhibition rates of 69.5% and 85.5% in ABTS•+ and DPPH• assays, respectively (IC₅₀ = 22 and 23.47 µg/mL). EH roots showed higher activity, reaching 89.4% and 78.2% inhibition (IC₅₀ = 21.8 and 20.72 µg/mL). Conversely, EM organs exhibited relatively lower radical scavenging capacities; however, EM leaves showed the highest α-glucosidase inhibition (49.1%). Overall, these results suggest that roots generally possess stronger antioxidant potential than leaves, whereas EM leaves stand out for their enzymatic inhibitory activity. These findings highlight the diverse phytochemical and bioactive profiles of E. beecheyanum, E. heterophyllum, and E. mexiae. 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, 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