We introduce a new flexible distribution four-parameter which is called [0,1]Truncated Exponentiated Exponential Burr type X distribution ([0,1] TEE-BX). Using binomial series expansion and exponential expansion, the new distribution is expanded by four parameters. We derive moments, moment generating function, quantile function, order statistics and the Rényi entropy. The maximum likelihood estimation method is used to estimate the parameters of the proposed TEE-BX model [0,1]. Finally, using two real-world data sets, the performance of the [0,1] TEE-BX distribution is explored. Based on the certain goodness of fit criteria, we conclude that the [0,1] TEE-BX distribution has a better fit than the other distributions.

In this paper, we introduce a novel family of continuous distributions known as the OddGeneralized Rayleigh-G Family. Within this family, we present a special sub-model known as the odd Generalized Rayleigh Inverse Weibull (OGRIW) distribution. The OGRIW distribution is derived by combining the T-X family and the Generalized Rayleigh distribution. We provide a comprehensive expansion of the (PDF) and (CDF) for the OGRIW distribution. Additionally, we investigate several mathematical properties of the OGRIW distribution, including moments, moment-generating function, incomplete moments, quantile function, order statistics and Rényi entropy. To estimate the model parameters, we employ the maximum likelihood method, aiming to identify the parameter values that maximise the likelihood of the observed data.Finally, we apply the proposed OGRIW distribution to two real COVID-19 datasets from Mexico and Canada. The results of these applications demonstrate that the new distribution exhibits remarkable flexibility and outperforms other comparative distributions in terms of accurately modelling the COVID-19 data.

In this paper, a new compound distribution termed as [0,1]Truncated Exponential Marshall-Olkin-Gompertz (TEMO-Go)is introduced. Several essential statistical properties of TEMO-Go distribution were studied. The estimation of distribution parameters was performed using the maximum likelihood estimation method, the flexibility of the new distribution was examined using two real data. The suitability of the proposed distribution indicates that it performs positively when compared to the existing distributions.

This study focuses on estimating the parameters of the Odd Burr XII–Exponential (OBXII‑E) distribution using both Bayesian and classical approaches. For the non‑Bayesian framework, seven estimation methods were considered: Maximum Likelihood, Least Squares, Weighted Least Squares, Maximum Product Space, Anderson–Darling, right‑Tailed Anderson–Darling, and Kolmogorov estimators. In the Bayesian context, parameter estimation was carried out using the Markov Chain Monte Carlo (MCMC) technique under different loss functions, including Squared Error, General Entropy, and Linear‑Exponential. Through extensive simulation experiments, the accuracy and consistency of each estimator were evaluated, revealing that all methods converge toward the true parameter values as sample size increases. The OBXII‑E distribution was further applied to two real datasets, where it consistently outperformed competing models based on multiple goodness‑of‑fit criteria. Overall, the results confirm the robustness and flexibility of the OBXII‑E distribution in modeling daily COVID-19 and carbon fibers data.

We introduce a new flexible four-parameter distribution called [0,1]Truncated Exponentiated Exponential Gompertz distribution ([0,1] TEE-Go). Several basic statistical properties of the [0,1] TEE-Go distribution have been studied. The parameters of the proposed [0,1] TEE-Go model were obtained at maximum Probability method. Two real data were adopted to illustrate the flexibility of [0,1] TEE-Go distribution. This flexibility enables the use of [0,1] TEE-Go distribution in various application areas.

Improving the statistical and predictive accuracy, especially of the data on natural hazards, is important in addressing these issues. Therefore, policymakers urgently need a reliable forecasting methodology that provides decision-makers with early estimates of future and resulting healthcare expenditures based on historical time series data, so that they can assess potential risks. Researchers in the field of time series face the problem of choosing the best model for analysis from among several available models. Hence, this study compares the most effective model between a time series structure and a neural network model. Therefore, this research compares the predictive performance of the seasonal Mixed Autoregressive and Moving Average models, and feed-forward neural networks using the Back Propagation algorithm. It includes applying these methods to real data representing monthly injuries and deaths resulting from natural hazards in the United States. The best model is determined using the MAE criterion for forecast accuracy by leaving the last 12 observations of the data series as an evaluation set to examine the predictive performance and perform a comparison to determine the most effective one.