Probability distributions have prominent applications in different sectors. Among these sectors, probability models are mostly used to analyze datasets in engineering. Among the existing probability distributions, the two-parameter Weibull model plays an important role in providing the best fit for engineering and other related datasets. This paper introduces a new method called a novel updated-W (denoted by “NU-W”) family of distributions that is used to develop a new updated form of the Weibull distribution. The proposed updated extension of the Weibull model is referred to as a novel updated Weibull (denoted as NU-Weibull) distribution. Distributional properties such as identifiability, heavy-tailed characteristic, and rth moment of the NU-W family are derived. The residual life analysis of the NU-Weibull distribution is provided. Finally, two physical applications from civil engineering and reliability sectors are analyzed to demonstrate the application and effectiveness of the NU-Weibull distribution. The data fitting results show that the NU-Weibull distribution is a more suitable and best fit for engineering datasets.

Theoretical and applied researchers have been frequently interested in proposing alternative skewed and symmetric lifetime parametric models that provide greater flexibility in modeling real-life data in several applied sciences. To fill this gap, we introduce a three-parameter bounded lifetime model called the exponentiated new power function (E-NPF) distribution. Some of its mathematical and reliability features are discussed. Furthermore, many possible shapes over certain choices of the model parameters are presented to understand the behavior of the density and hazard rate functions. For the estimation of the model parameters, we utilize eight classical approaches of estimation and provide a simulation study to assess and explore the asymptotic behaviors of these estimators. The maximum likelihood approach is used to estimate the E-NPF parameters under the type II censored samples. The efficiency of the E-NPF distribution is evaluated by modeling three lifetime datasets, showing that the E-NPF distribution gives a better fit over its competing models such as the Kumaraswamy-PF, Weibull-PF, generalized-PF, Kumaraswamy, and beta distributions.

This paper introduces a flexible three-parameter extension of the Lomax model called the odd Lomax–Lomax (OLxLx) distribution. The OLxLx distribution can provide left-skewed, symmetrical, right-skewed, and reversed-J shaped densities and increasing, constant, unimodal, and decreasing hazard rate shapes. Some mathematical properties of the introduced model are derived. The OLxLx density can be expressed as mixture of Lomax densities. The OLxLx parameters are estimated by using eight estimation methods and their performance is explored by using detailed simulation studies. The partial and overall ranks of the mean relative errors, absolute biases, and mean square errors of different estimators are presented to choose the best estimation method. The flexibility and applicability of the OLxLx distribution is shown using real-life medicine data, illustrating the superior fit of the OLxLx distribution over other competing Lomax distributions. The OLxLX distribution outperforms some rival Lomax distributions including the Kumaraswamy–Lomax, McDonald–Lomax, Weibull–Lomax, transmuted Weibull–Lomax, exponentiated-Lomax, Lomax–Weibull, modified Kies–Lomax, Burr X Lomax, beta exponentiated-Lomax, odd exponentiated half-logistic Lomax, and transmuted-Lomax distributions, among others.

This study introduces a new and flexible class of probability distributions known as the novel alpha-power X (NAP-X) family. A key development within this framework is the novel alpha-power half-logistic (NAP-HL) distribution, which extends the classical half-logistic model through an alpha-power transformation, allowing for greater adaptability to various data shapes. The paper explores several theoretical aspects of the proposed model, including its moments, quantile function and hazard rate. To assess the effectiveness of parameter estimation, a detailed simulation study is conducted using seven estimation techniques: Maximum likelihood estimation (MLE), Cramér–von Mises estimation (CVME), maximum product of spacings estimation (MPSE), least squares estimation (LSE), weighted least squares estimation (WLSE), Anderson–Darling estimation (ADE) and a right-tailed version of Anderson–Darling estimation (RTADE). The results offer comparative insights into the performance of each method across different sample sizes. The practical value of the NAP-HL distribution is demonstrated using two real datasets from the metrology and engineering domains. In both cases, the proposed model provides a better fit than the traditional half-logistic and related distributions, as shown by lower values of standard model selection criteria. Graphical tools such as fitted density curves, Q–Q and P–P plots, survival functions and box plots further support the suitability of the model for real-world data analysis.

A fully parametric family of distributions called the new generalized family (NGF) is proposed. The cumulative distribution function of the proposed NGF is constructed based on the reciprocal of the hazard rate function. Furthermore, a special sub-family called the new generalized Pareto (NGP) family is also addressed. A special sub-model of the NGP class called the new Kumaraswamy Pareto (NKP) distribution is introduced. The NKP model provides flexible shapes for its hazard and density functions. The properties of the NKP distribution are derived. In addition, the inferences under complete and bootstrapped samples of the NKP parameters are addressed. Monte Carlo simulation studies are also performed to explore the behavior of different estimators. Three real-life datasets are fitted using the NKP distribution, showing the superiority fit of the proposed statistical model.

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 significant monotonic 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.