In this article, a new three-parameter lifetime model called the Gull alpha power exponentiated exponential (GAPEE) distribution is introduced and studied by combining the Gull alpha power family of distributions and the exponentiated exponential distribution. The shapes of the probability density function (PDF) for the GAPEE distribution can be asymmetric shapes, like unimodal, decreasing, and right-skewed. In addition, the shapes of the hazard rate function (hrf) for the GAPEE distribution can be increasing, decreasing, and upside-down shaped. Several statistical features of the GAPEE distribution are computed. Eight estimation methods such as the maximum likelihood, Anderson-Darling, right-tail Anderson-Darling, left-tailed Anderson-Darling, Cramér-von Mises, least-squares, weighted least-squares, and maximum product of spacing are discussed to estimate the parameters of the GAPEE distribution. The flexibility and the importance of the GAPEE distribution were demonstrated utilizing three real-world datasets related to medical sciences. The GAPEE distribution is extremely adaptable and outperforms several well-known statistical models. A bivariate step-stress accelerated life test based on progressive type-I censoring using the model is presented. Minimizing the asymptotic variance of the maximum likelihood estimate of the log of the scale parameter at design stress under progressive type-I censoring yields an expression for the ideal test plan under progressive type-I censoring.

This paper presents a novel family of bivariate continuous Lomax generators known as the BFGMLG family, which is constructed using univariate Lomax generator (LG) families and the Farlie Gumbel Morgenstern (FGM) copula. We have derived several structural statistical properties of our proposed bivariate family, such as marginals, conditional distribution, conditional expectation, product moments, moment generating function, correlation, reliability function, and hazard rate function. The paper also introduces four special submodels of the new family based on the Weibull, exponential, Pareto, and log-logistic baseline distributions. The study establishes metrics for local dependency and examines the significant characteristics of the proposed bivariate model. To provide greater flexibility, a multivariate version of the continuous FGMLG family are suggested. Bayesian and maximum likelihood methods are employed to estimate the model parameters, and a Monte Carlo simulation evaluates the performance of the proposed bivariate family. Finally, the practical application of the proposed bivariate family is demonstrated through the analysis of four data sets.