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Introduction: This article introduces a new family of weighted mixture distributions, referred to as θ-WM. The θ-WM family is generated by combining two distributions weighted by a parameter θ, offering notable flexibility to model a wide range of complex phenomena. A special case study of the θ-weighted mixture distribution of Weibull-Lomax (θ-WMWLx) is included, resulting from the combination of Weibull and Lomax distributions. Methods: The research thoroughly examines the reliability and statistical properties of the θ-WMWLx distribution. Key aspects such as stochastic dominance, survival and hazard functions, mean residual life, and moments are addressed. The maximum likelihood method is used to estimate unknown parameters. Results: The research findings show that the θ-WMWLx distribution provides a superior fit compared to competing distributions. The analyses are validated using three real datasets, demonstrating the effectiveness of the proposed distribution. Discussion: The θ-WMWLx distribution stands out for its ability to model complex phenomena with high precision. Validation with real data confirms that the proposed distribution offers a better fit than existing distributions, highlighting its utility and applicability in various statistical analysis contexts. [ABSTRACT FROM AUTHOR]

This study proposes a new flexible family of distributions called the Lambert-G family. The Lambert family is very flexible and exhibits desirable properties. Its three-parameter special sub-models provide all significantmonotonic and non-monotonic failure rates. A special sub-model of the Lambert family called the Lambert-Lomax (LL) distribution is investigated. General expressions for the LL statistical properties are established. Characterizations of the LL distribution are addressed mathematically based on its hazard function. The estimation of the LL parameters is discussed using six estimation methods. The performance of this estimation method is explored through simulation experiments. The usefulness and flexibility of the LL distribution are demonstrated empirically using two real-life data sets. The LL model better fits the exponentiated Lomax, inverse power Lomax, Lomax-Rayleigh, power Lomax, and Lomax distributions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a parametric accelerated failure time (AFT) hazard-based regression model with the extended alpha-power exponential (EAPE) baseline distribution. The proposed model is called the extended alpha-power exponential-AFT (EAPE-AFT) regression model. We show that the EAPE distribution is closed under the AFT model. The parameters of the proposed EAPE-AFT model have been estimated by using the method of maximum likelihood estimation. An extensive simulation study was also conducted to examine the performance of the estimates under several scenarios based on the shapes of the baseline hazard function. Finally, real-life censored survival data has been used to illustrate the applicability of the proposed model. [ABSTRACT FROM AUTHOR]

This paper is presenting a new flexible probability distribution which named as Khalil new generalized exponential (KNGEx) distribution. We introduce its mathematical properties. The hazard function of the KNGEx distribution can be increasing, decreasing, and inverted bathtub. The parameters of the distribution are estimated using eight classical methods. Simulation studies based on complete sample are done. Finally, two applications to medicine and engineering data sets are presented. The analyzed data revealed that the proposed distribution could potentially be very useful in describing and modeling both data sets as compared to many other competing distributions. [ABSTRACT FROM AUTHOR]

In this paper, a new Kumaraswamy generalized family is proposed. Four sub-models of the proposed family accommodate symmetrical, left-skewed, bimodal, right-skewed unimodal, and reverse-J densities, as well as increasing, modified bathtub, decreasing, bathtub, upside down bathtub, reverse J and J shaped hazard rates. Its fundamental properties are derived. The maximum likelihood method and seven other methods are used for estimating the model parameters. Numerical simulations are performed to explore the performance of these estimation methods. Three real-life data sets from medicine, agriculture and engineering are fitted to illustrate the flexibility of the proposed family. The proposed family is a good alternative to the Kumaraswamy-G, beta-G, and Topp-Leone-G families. [ABSTRACT FROM AUTHOR]

Accelerated life tests have become increasingly important because of higher customer expectations for better reliability, more complicated products with more components, rapidly changing technologies advances, and the clear need for rapid product development. Hence, accelerated life tests have been widely used in manufacturing industries, particularly to obtain timely information on the reliability. Maximum likelihood estimation is the starting point when it comes to estimating the parameters of the model. In this paper, besides the method of maximum likelihood, nine other frequentist estimation methods are proposed to obtain the estimates of the exponentiated exponential distribution parameters under constant stress accelerated life testing. We consider two parametric bootstrap confidence intervals based on different methods of estimation. Furthermore, we use the different estimates to predict the shape parameter and the reliability function of the distribution under the usual conditions. The performance of the ten proposed estimation methods is evaluated via an extensive simulation study. As an empirical illustration, the proposed estimation methods are applied to an accelerated life test data set. [ABSTRACT FROM AUTHOR]