Search Results (43)

In this work, a type II Topp-Leone-G family of distributions is parametrically transformed to create a new flexible family of continuous probability distributions called exponentiated type II Topp-Leone-G distribution through exponentiation. A variety of density shapes and hazard rate behaviors, such as increasing, decreasing, bathtub, inverted bathtub-shaped, and unimodal forms, can be captured by the proposed family, which generalizes several current lifetime models. In addition to discussing significant special cases that correspond to well-known distributions, explicit expressions for the cumulative distribution function, probability density function, survival function, hazard rate function, quantile function, actuarial measures, and linear representation of the probability density function are derived. The maximum likelihood approach is used for parameter estimation, and the simulation study provides a brief discussion of the estimator’s asymptotic characteristics. Kolmogorov–Smirnov and Cramer–Von Mises goodness-of-fit metrics and their p-values, along with information criteria like Akaike Information Criterion, Bayesian Information Criterion, Consistent Akaike Information Criterion, and Hannan–Quinn Information Criterion, are used to evaluate the appropriateness of the model. Furthermore, to visually assess model performance, graphical diagnostic techniques, such as density and distribution function overlays, quantile–quantile plots, and probability–probability plots, are used. Real-life datasets are analyzed to show the applicability of the exponentiated type II Topp-Leone-G family using Weibull distribution as the baseline, and its performance is compared with some other competing distributions. The findings demonstrate the potential utility of the proposed model in the areas of insurance and related applied domains by showing that it fits better than the competing models considered. Full article

In this paper, we introduce a new extension of the Topp–Leone-G family, called the generalized Marshall–Olkin Topp–Leone-G (GMOTL-G) family of distributions. The proposed family is obtained by combining the generalized Marshall–Olkin and Topp–Leone-G generators, leading to a more flexible class of models for lifetime data. We study several of its mathematical and statistical properties and focus in particular on the generalized Marshall–Olkin Topp–Leone exponential (GMOTL-E) distribution as an important special case. For this model, we derive and discuss a number of useful characteristics, including the moment generating function, moments, order statistics, residual and reversed residual life functions, mean deviations, asymptotic behavior, and stochastic ordering. We also develop maximum likelihood estimation for the model parameters under both complete and right-censored samples. In addition, we construct a goodness-of-fit test for the proposed model under independent right censoring using a chi-square type approach. The performance of the estimation and testing procedures is investigated through simulation, and the results show good behavior of the estimators and satisfactory agreement between empirical and theoretical significance levels. Finally, two real data applications, one with complete data and one with right-censored data, are presented to illustrate the flexibility and practical usefulness of the proposed model. These results show that the new family provides an effective tool for modeling lifetime data and for assessing model adequacy in the presence of right censoring. Full article

This work presents a new family of distributions (FoDs) called the exponentiated half logistic-generalized-Topp-Leone-G (EHL-GEN-TL-G) family. This family can be expressed as an infinite linear combination of exponentiated-G densities, which facilitates the derivation of its important statistical properties. The shapes of the density and hazard rate functions were investigated for special cases. The model parameters were estimated using six different methods, with the maximum likelihood technique emerging as the best approach. The consistency of the parameter estimates was then validated through Monte Carlo simulations. The exponentiated half logistic-generalized-Topp-Leone-Weibull (EHL-GEN-TL-W) distribution, a sub-model of the EHL-GEN-TL-G family, was applied to three sets of engineering failure time data. The results indicated that, based on in-sample goodness-of-fit criteria, the EHL-GEN-TL-W model provided the best fit among the several established models considered. Additionally, the EHL-GEN-TL-W regression model was developed, and its practical utility in modeling failure data was demonstrated. Full article

This study is a detailed study of unit J-shaped distributions which establishes and examines the unit Topp–Leone distribution. The proposed study presents a mathematically tractable model of bounded data with strong skewness and boundary effects. Various basic distributional properties, such as moments, entropy measures, order statistics, and L-moments, are obtained in explicit form, which provides a full analytic description of the model. Type-II censoring is applied to develop some statistical inferential methods. The usefulness of the suggested distribution is illustrated by the application to the normalized water use efficiency indicators and censored survival time data. The findings are useful to the theory of unit distributions, as they introduce new analytics that have been demonstrated to be beneficial in practice and demonstrate that the theory is effective in applications with limited and censored data. Full article

This study introduces a novel four-parameter lifetime distribution constructed within the Topp–Leone Power Gompertz framework. Owing to its flexible structure, the proposed model accommodates a wide range of density shapes and hazard-rate patterns, including increasing, decreasing, bathtub-shaped, unimodal, and other non-monotone behaviors. Key distributional properties, including moments, entropy-based measures, quantile-based measures, and order statistics, are derived. Parameter inference is conducted using both likelihood-based and Bayesian approaches, and the finite-sample performance of the resulting estimators is assessed via Monte Carlo simulations. The practical relevance of the proposed distribution is illustrated using two real datasets and benchmarked against several competing lifetime models, including the Gompertz, Power Gompertz, Weibull, Topp–Leone Gompertz, Marshall–Olkin Gompertz, and Exponentiated Gompertz distributions. Overall, the comparative analyses demonstrate the superior fitting performance of the proposed model, highlighting its effectiveness for complex reliability, survival, and pharmacokinetic data. Full article

A new generalized family of distributions, termed the Cosine–Topp–Leone–Exponentiated Half Logistic–G (Cos–TL–EHL–G) family, is proposed. The primary motivation for introducing this family is to enhance the modelling flexibility of the existing Cosine–Topp–Leone–G class by incorporating a exponentiated half logistic (EHL-G)-based transformation. Two important special cases, namely the Cos–TL–EHL–Weibull (Cos–TL–EHL–W) and Cos–TL–EHL–Log–Logistic (Cos–TL–EHL–LLoG) distributions, are presented. Several mathematical and statistical properties of the proposed family are derived, including series expansions, moments, order statistics, and uncertainty measures. Parameter estimation is carried out using maximum likelihood, least squares, Anderson–Darling, and Cramér–von Mises methods. A Monte Carlo simulation study indicates that the maximum likelihood estimator outperforms the competing estimation techniques. The practical usefulness and robustness of the proposed family are illustrated through applications to two real datasets, where the Cos–TL–EHL–W distribution demonstrates superior performance compared to both nested and non-nested competing models. Full article

This article introduces a new flexible distribution, called the alpha power Topp–Leone Dagum (APTLDa) distribution, which extends the classical Dagum model by combining the Topp–Leone generator with the alpha power transformation (APT). The proposed distribution is capable of modeling data with symmetrical and asymmetrical shapes for the probability density and hazard rate functions. This makes it suitable for lifetime and reliability data analysis. Several important statistical properties of the new distribution are derived, including the quantile function, moments, entropy measures, order statistics, and reliability-related functions. Parameter estimation is carried out using the maximum likelihood method, and the performance of the estimators is examined through an extensive simulation study under different sample sizes and parameter settings. The simulation results demonstrate the consistency and good finite-sample behavior of the estimators. The practical usefulness of the proposed distribution is illustrated through applications to two real datasets, where its performance is compared with several competing models. The results show that the APTLDa distribution provides a flexible and effective alternative for modeling lifetime data. Full article

This article defines an inverted Topp–Leone distribution. Several mathematical properties and maximum likelihood estimation of parameters of this distribution are considered. The shape of the distribution for different sets of parameters is discussed. Several mathematical properties such as the cumulative distribution function, mode, moment-generating function, survival function, hazard rate function, stress-strength reliability R, moments, Rényi entropy, Shannon entropy, Fisher information matrix, and partial ordering associated with this distribution, have been derived. Distributions of the sum and quotient of two independent inverted Topp–Leone variables have also been obtained. Full article

This paper introduces the Topp–Leone Heavy-Tailed Odd Burr X-G (TL-HT-OBX-G) family of distributions (FOD), designed to model diverse data patterns. The new distribution is an infinite linear combination of the established exponentiated-G distributions. We used the established properties of the exponentiated-G distribution to infer the properties of the new FOD. The properties considered include the quantile function, moments and moment generating functions, probability-weighted moments, order statistics, stochastic orderings, and Rényi entropy. Parameter estimation is performed using multiple techniques, such as maximum likelihood, least squares, weighted least squares, Anderson–Darling, Cramér–von Mises, and Right-Tail Anderson–Darling. The maximum likelihood estimation method produced superior results in the Monte Carlo simulation studies. A special case of the developed model was applied to three real-world datasets. The model parameters were estimated using the maximum likelihood method. The selected special model was compared to other competing models, and goodness-of-fit was evaluated by the use of several goodness-of-fit statistics. The developed model fit the selected real-world datasets better than all the selected competing models. The new FOD provides a new framework for data modeling in health sciences and reliability datasets. Full article

The acceptance of generalized distributions has significantly improved over the past two decades. In this paper, we introduce a new generalized distribution: Topp–Leone odd Weibull flexible-G family of distributions (FoD). The new FoD is a combination of two FOD; the Topp–Leone-G and odd Weibull-flexible-G families. The proposed FoD possesses more flexibility compared to the two individual FoD when considered separately. Some selected statistical properties of this new model are derived. Three special cases from the proposed family are considered. The new model exhibits symmetry and long or short tails, and it also addresses various levels of kurtosis. Monte Carlo simulation studies were conducted to verify the consistency of the maximum likelihood estimators. Two real data examples were used as illustrations on the flexibility of the new model in comparison to other competing models. The developed model proved to perform better than all the selected competing models. Full article

As part of this study, we design a reliability acceptance sampling plan under the assumption that the lifetime of a product follows the Topp–Leone generated Weibull (TLGW) distribution, a model that exhibits structural symmetry in its hazard rate behavior and distributional form. The fundamental procedures for constructing such a plan are described. We compute and tabulate the minimum sample sizes required for given risk criteria using both binomial and Poisson models for the number of failures. We also provide the operating characteristic (OC) values for the proposed sampling plans, and determine the minimum ratios of true mean life to specified mean life needed to satisfy a given producer’s risk. The role of symmetry in the TLGW distribution is highlighted in its balanced tail properties and shape characteristics, which influence the performance of the acceptance sampling plan. Finally, we illustrate the applicability of the proposed plan with real-world data. Full article

In lifetime testing, the failure times of highly reliable products under normal usage conditions are often impractically long, making direct reliability assessment impractical. To overcome this, step-stress partially accelerated life testing is employed to reduce testing time while preserving data quality. This paper develops a Bayesian model based on Type II censored data, assuming that item lifetimes follow the Topp–Leone inverted Kumaraswamy distribution, a flexible alternative to classical lifetime models due to its ability to capture various hazard rate shapes and to model bounded and skewed lifetime data more effectively than traditional models observed in real-world reliability data. Bayes estimators of the model parameters and acceleration factor are derived under both symmetric (balanced squared error) and asymmetric (balanced linear exponential) loss functions using informative priors. The novelty of this work lies in the integration of the Topp–Leone inverted Kumaraswamy distribution within the Bayesian step-stress partially accelerated life testing framework, which has not been explored previously, offering improved modeling capability for complex lifetime data. The proposed method is validated through comprehensive simulation studies under various censoring schemes, demonstrating robustness and superior estimation performance compared to traditional models. A real-data application involving COVID-19 mortality data further illustrates the practical relevance and improved fit of the model. Overall, the results highlight the flexibility, efficiency, and applicability of the proposed Bayesian approach in reliability analysis. Full article

In this paper, two different families are mixed: the exponentiated and new Topp–Leone-G families. This yields a new family, which we named the mixture of the exponentiated and new Topp–Leone-G family. Some statistical properties of the proposed family are obtained. Then, the mixture of two exponentiated new Topp–Leone inverse Weibull distribution is introduced as a sub-model from the mixture of exponentiated and new Topp–Leone-G family. Some related properties are studied, such as the quantile function, moments, moment generating function, and order statistics. Furthermore, the maximum likelihood and Bayes approaches are employed to estimate the unknown parameters, reliability and hazard rate functions of the mixture of exponentiated and new Topp–Leone inverse Weibull distribution. Bayes estimators are derived under both the symmetric squared error loss function and the asymmetric linear exponential loss function. The performance of maximum likelihood and Bayes estimators is evaluated through a Monte Carlo simulation. The applicability and flexibility of the MENTL-IW distribution are demonstrated by well-fitting two real-world engineering datasets. The results demonstrate the superior performance of the MENTL-IW distribution compared to other competing models. Full article

This study introduces the DUS Topp–Leone family of distributions, a novel extension of the Topp–Leone distribution enhanced by the DUS transformer. We derive the cumulative distribution function (CDF) and probability density function (PDF), demonstrating the distribution’s flexibility in modeling various lifetime phenomena. The DUS-TL exponential distribution was studied as a sub-model, with analytical and graphical evidence revealing that it exhibits a unique unimodal shape, along with fat-tail characteristics, making it suitable for time-to-event data analysis. We evaluate parameter estimation methods, revealing that non-Bayesian approaches, particularly Maximum Likelihood and Least Squares, outperform Bayesian techniques in terms of bias and root mean square error. Additionally, the distribution effectively models datasets with varying skewness and kurtosis values, as illustrated by its application to total factor productivity data across African countries and the mortality rate of people who injected drugs. Overall, the DUS Topp–Leone family represents a significant advancement in statistical modeling, offering robust tools for researchers in diverse fields. Full article

Abstract: This paper is concerned with applying the Bayesian and E-Bayesian approaches to estimating the unknown parameters of the modified Topp–Leone–Chen distribution under a progressive Type-II censored sample plan. The paper explores the complexities of different estimating methods and investigates the behavior of the estimates through some computations. The Bayes and E-Bayes estimators are obtained under two distinct loss functions, the balanced squared error loss function, as a symmetric loss function, and the balanced linear exponential loss function, as an asymmetric loss function. The estimators are derived using gamma prior and uniform hyperprior distributions. A numerical illustration is given to examine the theoretical results through using the Metropolis–Hastings algorithm of the Markov chain Monte Carlo method of simulation by the R programming language. Finally, real-life data sets are applied to prove the flexibility and applicability of the model. Full article