In this study, we designed a new family of distributions called new odd reparameterized exponential transformed-X family of distributions. This was achieved by utilizing an exponential distribution with a constant scale parameter as the transformer and then the odd function of the baseline distribution as the generalizer. The new family was used to extend the classical Weibull distribution. We further studied the characteristics of the new extended Weibull distribution which include the quantile function, moment, moment generating function, mean residual life function, order statistic, entropy and extropy. Again, the parameters were estimated using both non-Bayesian and Bayesian approaches. A comprehensive Monte Carlo simulation was conducted under four different scenarios. The proposed distribution was fitted to HIV/AIDS and COVID-19 data and then compared with the baseline distribution (Weibull) and other related models. The new distribution commands superior fit with a probability value of 0.9959 and 0.7086 in the two datasets respectively.

This paper introduces the updated Lindley (UL) distribution, an innovative mixture of exponential and gamma distributions designed to model lifetime data with various failure rate patterns. The statistical properties of the UL distribution, including moments, skewness, kurtosis, and tail behavior, are thoroughly examined to highlight its flexibility and applicability. Parameter estimation methods using non-Bayesian are evaluated for their accuracy using bias and mean squared error metrics across various scenarios. The paper further explores applications of the UL distribution in acceptance sampling plans, actuarial risk assessment, and reliability analysis. Comprehensive simulation studies and graphical visualizations underscore the robustness and versatility of the distribution in addressing real-world problems, making it a valuable tool in statistical modeling and decision-making processes.

This article is an extension of the Chris-Jerry distribution (C-JD) in that a two-parameter Chris-Jerry distribution (TPCJD) is suggested and its characteristics are studied. Based on the determined domain of attraction and other major statistical properties, the proposed TPCJD seems to fit into the Gumbel domain. Additionally, it has been confirmed that the stress strength is reliable. The tail study suggests that the TPCJD’s substantial tail makes it suited for a range of applications. The study took into account the single acceptance sampling approach using both simulation and real-life situations. The parameters of the TPCJD were estimated by some classical and Bayesian approaches. The mean squared errors (MSE), linear-exponential, and generalized entropy loss functions were deployed to obtain the Bayesian estimators aided by the Markov chain Monte Carlo (MCMC) simulation. An analysis of lifetime data on two events justified the use of the proposed distribution after comparing the results with some standard lifetime models.

This paper introduces the novel, single-parameter Obulezi distribution for modeling lifetime data. We derived its statistical and reliability properties and performed an exhaustive comparison of fifteen parameter estimation techniques via simulation and application to three real datasets. Simulation results confirmed the consistency of all estimators, while empirical analysis showed the Obulezi distribution consistently yielded the lowest standard errors, proving it to be the most precise and stable model compared to competitors. Goodness-of-fit metrics confirmed the \texttt{Obulezi} distribution's superior fit, particularly for data exhibiting an increasing hazard rate. The Obulezi distribution is thus a robust and highly competitive model for parsimonious survival and reliability analysis.

A novel lifetime distribution has been defined and examined in this study. The odd Lindley–Pareto (OLiP) distribution is the name we give to the new distribution. The new density function can be written as an odd Lindley-G distribution with Pareto amplification. The moment-generating function and characteristic function, entropy and asymptotic behavior, order statistics and moments, mode, variance, skewness, and kurtosis are some of the aspects of the OLiP distribution that are discovered. Seven non-Bayesian estimation techniques and Bayesian estimation utilizing Markov chain Monte Carlo were compared for performance. Additionally, when the lifetime test is truncated after a predetermined period, single acceptance sampling plans (SASPs) are created for the newly suggested, OLiP distribution. The median lifetime of the OLiP distribution with pre-specified factors is taken as the truncation time. To guarantee that the specific life test is obtained at the defined risk to the user, the minimum sample size is required. For a particular consumer’s risk, the OLiP distribution’s parameters, and the truncation time, numerical results are obtained. The new distribution is illustrated using mortality rates of COVID-19 patients in Canada and vinyl chloride data in (g/L) from ground-water monitoring wells that are located in clean-up-gradient areas.