In the last decade, the size and complexity of datasets have expanded significantly, necessitating more sophisticated predictive methods. Despite this growth, limited research has been conducted on the effects of autocorrelation within widely used regression methods. This study addresses this gap by investigating how autocorrelation impacts the predictive accuracy and efficiency of six regression approaches: Artificial Neural Network (ANN), Ordinary Least Squares (OLS), Cochrane–Orcutt (CO), Prais–Winsten (PW), Maximum Likelihood Estimation (MLE), and Restricted Maximum Likelihood Estimation (RMLE). The study evaluates each method’s performance on three datasets characterized by autocorrelation, comparing their predictive accuracy and variability. The analysis is structured into three phases: the first phase examines predictive accuracy across methods using Mean Squared Error (MSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE); the second phase evaluates the efficiency of parameter estimation based on standard errors across methods; and the final phase visually assesses the closeness of predicted values to actual values through scatter plots. The results indicate that the ANN consistently provides the most accurate predictions, particularly in large sample sizes with extensive training data. For GDP data, the ANN achieved an MSE of 1.05 × 10⁹, an MAE of 23,344.64, and an MAPE of 81.66%, demonstrating up to a 90% reduction in the MSE compared to OLS. These findings underscore the advantages of the ANN for predictive tasks involving autocorrelated data, highlighting its robustness and suitability for complex, large-scale datasets. This study provides practical guidance for selecting optimal prediction techniques in the presence of autocorrelation, recommending the ANN as the preferred method due to its superior performance.

Hypothesis tests are essential tools in applied statistics, but their results can vary when repeated. The reproducibility probability (RP) quantifies the probability of obtaining the same test outcome—either rejecting or not rejecting the null hypothesis—if a hypothesis test is repeated under identical conditions. In this paper, we apply the parametric predictive bootstrap (PP-B) method to evaluate the reproducibility of parametric tests and compare it with the nonparametric predictive bootstrap (NPI-B) method. The explicitly predictive nature of both methods aligns well with the concept of RP. Simulation studies demonstrate that PP-B provides RP values with less variability than NPI-B, benefiting from the assumed parametric model. The bootstrap approach offers a flexible framework for assessing test reproducibility and can be extended to a wide range of parametric tests.

The complexity of inflation rate fluctuations poses a significant challenge to traditional statistical models, requiring the development of more dependable and adaptable methods. The primary objectives of this paper are to predict and model inflation rate data. We propose the novel Fréchet (NF) via the logarithmic transformation approach from the conventional Fréchet distribution. Its density function might be nearly symmetric, bimodal, right‐skewed, or left‐skewed. The hazard function of the NF distribution is highly flexible, capable of increasing, decreasing, being upside‐down bathtub‐shaped, or increasing‐decreasing, which is not possible with the traditional Fréchet distribution. We derive key statistical features of this distribution and obtain parameter estimates using various estimation methods. Monte Carlo simulations are used to demonstrate the accuracy of the parameter estimates. The potential of the NF distribution is empirically validated using monthly inflation rate data. Additionally, we conduct a comparative analysis of various time series approaches using statistical methods as well as machine learning models for predicting inflation rates, including ARIMA, recurrent neural networks (RNN), and support vector regression (SVR). The findings reveal that SVR outperforms other methods by achieving the lowest errors across all metrics, with a root mean squared error (RMSE) of 0.2225, a mean absolute error (MAE) of 0.1394, and a mean absolute percentage error (MAPE) of 0.020101, underscoring its effectiveness in modeling and predicting inflation rate data.

In this paper, we introduce and study the length‐biased Garhy distribution (LBGD), a novel one‐parameter weighted extension of the Garhy distribution (GD) using the length‐biased class of distributions. The LBGD offers enhanced flexibility for modeling positively skewed and heavy‐tailed data commonly encountered in environmental analysis. Some important closed‐form expressions for seven different extropy measures, such as classical extropy, weighted extropy, residual extropy, weighted residual extropy, past extropy, weighted past extropy, and cumulative residual extropy, are computed for the LBGD. In addition, several closed‐form statistical properties, including mode, ordinary moments, mean, variance, moment generating function, and incomplete moments, are calculated. Parameter and extropy estimations are performed via maximum likelihood estimation methodology and are investigated. An extensive Monte Carlo simulation study evaluates the performance of the maximum likelihood estimator, as well as the estimators for all seven extropy measures, in terms of bias, mean squared error, root mean squared error, average interval length, and coverage probability. The importance, applicability, and superiority of the suggested LBGD are demonstrated through application to real environmental data. The LBGD consistently outperforms 15 well‐known competing statistical distributions—such as LB weighted Ishita, Akash, Ishita, Pranav, Rama, half‐logistic exponential, half‐logistic Pareto, Xgamma, Chris‐Jerry, Zeghdoudi, Shukla, Lindley, XLindley, Komal, and GD distributions—across several model selection criteria, goodness‐of‐fit tests, and extropy measure‐based comparisons, confirming its potential as a valuable tool for analyzing positively skewed data.

This paper introduces a novel and flexible class of continuous probability distributions, termed the Alpha Power Survival Ratio-X (APSR-X) family. Unlike many existing transformation-based families, the APSR-X class integrates an alpha power transformation with a survival ratio structure, offering a new mechanism for enhancing shape flexibility while maintaining mathematical tractability. This construction enables fine control over both the tail behavior and the symmetry properties, distinguishing it from traditional alpha power or survival-based extensions. We focus on a key member of this family, the two-parameter Alpha Power Survival Ratio Exponential (APSR-Exp) distribution, deriving essential mathematical properties including moments, quantile functions and hazard rate structures. We estimate the model parameters using eight frequentist methods: the maximum likelihood (MLE), maximum product of spacings (MPSE), least squares (LSE), weighted least squares (WLSE), Anderson–Darling (ADE), right-tailed Anderson–Darling (RADE), Cramér–von Mises (CVME) and percentile (PCE) estimation. Through comprehensive Monte Carlo simulations, we evaluate the estimator performance using bias, mean squared error and mean relative error metrics. The proposed APSR-X framework uniquely enables preservation or controlled modification of the symmetry in probability density and hazard rate functions via its shape parameter. This capability is particularly valuable in reliability and survival analyses, where symmetric patterns represent balanced risk profiles while asymmetric shapes capture skewed failure behaviors. We demonstrate the practical utility of the APSR-Exp model through three real-world applications: economic (tax revenue durations), engineering (mechanical repair times) and medical (infection durations) datasets. In all cases, the proposed model achieves a superior fit over that of the conventional alternatives, supported by goodness-of-fit statistics and visual diagnostics. These findings establish the APSR-X family as a unique, symmetry-aware modeling framework for complex lifetime data.

This study introduces a new continuous probability distribution, termed the extended bounded sine hyperbolic (EBSH) distribution, for modeling non-negative data with flexible structural properties. The distribution accommodates symmetric and skewed behaviors and captures a wide range of hazard rate patterns, including increasing, decreasing, and bathtub-shaped forms. Beyond its theoretical contribution, the study investigates the use of the EBSH distribution as a feature engineering mechanism in machine learning. Raw input variables are transformed through the EBSH formulation to enhance data representation and improve predictive performance. The approach is evaluated using COVID-19 mortality and breast cancer datasets, using models such as recurrent neural networks (RNN) and support vector regression (SVR). Experimental results indicate that EBSH-based feature engineering improves prediction accuracy compared to raw features. For the COVID-19 dataset, the RNN model achieved a mean absolute error (MAE) of 0.0296 and a root mean square error (RMSE) of 0.0373 using raw features, which further reduced to approximately 0.0251 (MAE) and 0.0328 (RMSE) after applying EBSH-based transformations. Similarly, for the breast cancer dataset, SVR produced an MAE of 4.0177 and an RMSE of 4.9926 with raw features, improving to about 3.6842 and 4.5213, respectively, under the engineered feature space. These findings demonstrate that the proposed EBSH distribution not only provides a flexible statistical modeling approach but also serves as an effective feature engineering tool that enhances machine learning performance across real-world datasets.