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.

In this paper, a new one-parameter distribution named Chris-Jerry is suggested from two component mixture of Exponential (\(\theta\)) distribution and Gamma(3; \(\theta\)) distribution with mixing proportion \(p=\frac{\theta}{\theta + 2}\) having a flexibility advantage in modeling lifetime data. The statistical properties are discussed and the maximum likelihood estimation procedure is used to obtain the parameter estimate. The Convolution of the product of Pareto random variable with the proposed Chris-Jerry distributed random variable is explored with its marginal density derived. To illustrate the usefulness, three sets of lifetime data are employed and LL, AIC, BIC and K-S statistics are obtained for Exponential, Ishita, Akash, Rama, Pranav, Rani, Lindley, Sujatha, Aradhana, Shanker and XGamma and the Chris-Jerry distributions.

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.

In this study, we introduce the "Power Chris-Jerry" distribution, conducting a comprehensive analysis of its fundamental mathematical characteristics and an extensive exploration of various crucial aspects. These encompass investigations into its mode, quantile function, moments, coefficient of skewness, kurtosis, moment generating function, stochastic ordering, distribution of order statistics, reliability analysis, and mean past lifetime. Furthermore, we provide an in-depth assessment of four distinct parameter estimation methodologies: maximum likelihood estimation (MLE), Least Squares (LS), maximum product spacing method (MPS), and the Method of Cram`er-von-Mises (CVM). Our investigation uncovers a consistent pattern wherein the MLE, LS, and CVM approaches consistently yield underestimated parameter values. Intriguingly, we observe a consistent trend of decreasing Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and BIAS across all estimation techniques as sample sizes increase. Remarkably, our simulation results consistently favor the Maximum Product Spacing (MPS) method, highlighting its superiority in generating estimates with smaller MSE values across a broad spectrum of parameter values and sample sizes. These findings emphasize the robustness and dependability of the MPS estimator, offering valuable insights and practical guidance for both practitioners and researchers engaged in probability distribution modeling.

Breaking away from traditional methods, this study investigates the asymmetric effects of macroeconomic shocks on economic growth in Nigeria using a novel Machine Learning-Augmented Nonlinear Autoregressive Distributed Lag (NARDL) model. We utilized a Random Forest algorithm to data-driven feature selection, thus model optimization and its enhanced robustness against random selection of lags. The results confirm the presence of a long-run cointegrating relationship and show that positive and negative oil price shocks statistically differ in their effects on GDP. We also find inflation to have a strong negative long-run effect, and government capital expenditure is a significant driver of growth. Such embedding of machine learning in the NARDL model is a more empirically valid policy analysis tool that supplies key findings for policymakers in resource-dependent economies.

Due to variations in life occurrences, descriptions or interpretations and predictions with some level of accuracy has become challenging. In order to use models to solve these problems, statisticians have provided numerous number of probability distributions which can be used to describe one situation or the other. Rama shanker provided Shanker distribution which is not flexible enough to accommodate datasets with decreasing function. In order to add flexibility to Shankers’ distribution, the aim of this article is to suggest a new model developed by modifying shankers’ distribution. The new distribution will be called “Modified inverse Shanker distribution”. It has one special case, inverse Shanker distribution. Besides the basic properties of the distribution, the maximum likelihood technique of estimating the parameters of the distribution and some of the reliability measures are also discussed. We also illustrate the applicability of the proposed distribution using two real datasets.