This article examines the new inverse unit exponential distribution, utilizing both classical and Bayesian methodologies; it begins by presenting the general properties of the proposed model, highlighting characteristic features, such as the presence of a reverse-J or increasing and inverted bathtub-shaped hazard rate function. Furthermore, it explores various statistical properties of the suggested distribution. It employs 12 methods to estimate the associated parameters. A Monte Carlo simulation is conducted to evaluate the accuracy of the estimation procedure. Even for small samples, the results indicate that biases and mean square errors decrease as the sample size increases, demonstrating the robustness of the estimation method. The application of the suggested distribution to real datasets is then discussed. Empirical evidence, using model selection criteria and goodness-of-fit test statistics, supports the assertion that the suggested model outperforms several existing models considered in the study. This article extends its analysis to the Bayesian framework. Using the Hamiltonian Monte Carlo with the no U-turn sampling algorithm, 8000 real samples are generated. The convergence assessment reveals that the chains are convergent and the samples are independent. Subsequently, using the posterior samples, the parameters of the proposed model are estimated, and credible intervals and highest posterior density intervals are computed to quantify uncertainty. The applicability of the suggested model to real data under both classical and Bayesian methodologies provides insights into its statistical properties and performance compared to existing models.

This paper introduces the power new XLindley (PNXL) distribution, a novel two-parameter distribution derived using the power transformation method applied to the XLindley distribution. We thoroughly explore the structural properties of the PNXL distribution, including the rth moment about the origin, moment generating function, survival rate function, distribution function, hazard rate function, skewness, kurtosis, and coefficient of variation. Additionally, we derive the quantile function, fuzzy reliability, reliability measures, stochastic ordering, and actuarial measures for this new distribution. To estimate the parameters of the PNXL distribution, we propose several estimators and evaluate their performance through extensive simulation studies. To demonstrate the applicability and superiority of the PNXL distribution over existing distributions, we fit it to two real datasets and compare its performance with potential competing models. The results highlight the PNXL distribution's effectiveness and potential as a robust tool for modeling and analyzing real-world data.

This paper introduces a new lifetime distribution by mixing the first two lower record values and various distributional properties are examined. Statistical inference on distribution parameters are discussed with five estimators. A Monte Carlo simulation study is carried out to evaluate the risk behavior of these estimators for different sample of sizes. The distribution modeling analysis is provided based on real data to demonstrate the fitting ability of the proposed model. In addition, a lifetime regression model is described by reparameterization on the log lifetimes. The superiority of proposed regression model is revealed in well-known models.

In this study, we introduce a new lifetime distribution by using quadratic rank transmutation map. The some properties of this new distribution is provided. Furthermore, the parameters of this new distribution are estimated by the maximum likelihood method. The performances of the estimates are examined according to mean squared error (MSE) criteria through a Monte Carlo simulation study. Finally a real data applications are presented to evaluate the fits of introduced distribution.

Poisson regression is used to deal with count data. The Poisson regression ratio estimator of the population mean is extended from single to double sampling. This is made possible by the provision of the population mean of an auxiliary variable. The mean square errors of the proposed estimators are expressed up to the first order. Theoretical and numerical results demonstrate that the proposed double-sampling Poisson-regression ratio estimator has a lower mean square error than the double-ratio and the single-sampling estimator. For Covid-19, the minimum mean square errors yielded by the proposed estimator of the total number of cases are 0.095 cases per day and 67.8 cases, compared with 0.112 cases per day and 84.8 cases with the double-ratio estimator.