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HIV (Human Immunodeficiency Virus) is a virus that causes the immune system to be damaged, thereby reducing the body’s ability to defend against infections and illnesses. In the absence of proper treatment, HIV can culminate into AIDS (Acquired Immunodeficiency Syndrome). The first-line approach to HIV infection consists of antiretroviral therapy (ART), a combination of drugs that restrict virus replication. Effective prediction of infectious diseases is particularly vital for timely interventions and allocation of resources for disease management and prevention. This study focuses on identifying effective time series forecasting models for HIV and anti-retroviral therapy (ART) cases in Pakistan. The study utilized monthly reported HIV and ART cases data from the National AIDS Control Program, sourced from the Pakistan Bureau of Statistics, spanning the period from 2016 to 2021. Various time series models including ARIMA (Auto-regressive integrated moving average), exponential smoothing (Brown, Holt, Winter), neural network auto-regressive model (NNAR), and ETS (Exponential Smoothing State space) models were applied to analyze and forecast the monthly patterns of HIV and ART cases. Descriptive and time series analyses were conducted using the R programming language. The models were evaluated based on their ability to accurately capture and predict the fluctuations in HIV and ART cases over time. The average monthly cases for HIV and ART were found to be 36,405 ± 12,740 and 28,287 ± 12,485, respectively. Among the models evaluated, the NNAR (1,1,2) forecasting model emerged as the most accurate for both HIV and ART cases. It outperformed other competing models based on well-known accuracy measures such as RMSE, MAE, and MAPE. According to the selected NNAR(1,1,2) model, the study predicts a monthly increase of 4.98% in HIV cases and 16.32% in ART cases. The results proposed the non-linear approach of NNAR model to predict the AIDS and ART cases which help policymakers and healthcare professionals involved in disease management and prevention strategies in Pakistan to improve the policies and their implementation.

Gross domestic product (GDP) serves as a crucial economic indicator for measuring a country's economic growth, exhibiting both linear and non-linear trends. This study aims to analyze and propose an efficient and accurate time series approach for modeling and forecasting the GDP annual growth rate (%) of Saudi Arabia, a key financial indicator of the country. Stochastic linear and non-linear time series modeling, along with hybrid approaches, are employed and their results are compared. Initially, conventional linear and nonlinear methods such as ARIMA, Exponential smoothing, TBATS, and NNAR are applied. Subsequently, hybrid models combining these individual time series approaches are utilized. Model diagnostics, including mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE), are employed as criteria for model selection to identify the best-performing model. The findings demonstrated that the neural network autoregressive (NNAR) model, as a non-linear approach, outperformed all other models, exhibiting the lowest values of MAE, RMSE and MAPE. The NNAR(5,3) projected the GDP of 1.3% which is close to the projection of IMF benchmark (1.9) for the year 2023. The selected model can be employed by economists and policymakers to formulate appropriate policies and plans. This quantitative study provides policymakers with a basis for monitoring fluctuations in GDP growth from 2022 to 2029 and ensuring the sustained progression of GDP beyond 2029. Additionally, this study serves as a guide for researchers to test these approaches in different economic dynamics.

For the first time, ten frequentist estimation methods are considered on stress-strength reliability R = P(Y < X) when X and Y are two independent Weibull distributions with the same shape parameter. The start point to estimate the parameter R is the maximum likelihood method. Other than the maximum likelihood method, a nine frequentist estimation methods are used to estimate R, namely: least square, weighted least square, percentile, maximum product of spacing, minimum spacing absolute distance, minimum spacing absolute-log distance, method of Cramér-von Mises, Anderson-Darling and Right-tail Anderson-Darling. We also consider two parametric bootstrap confidence intervals of R. We compare the efficiency of the different proposed estimators by conducting an extensive Mont Carlo simulation study. The performance and the finite sample properties of the different estimators are compared in terms of relative biases and relative mean squared errors. The Mont Carlo simulation study revels that the percentile and maximum product of spacing methods are highly competitive with the other methods for small and large sample sizes. To show the applicability and the importance of the proposed estimators, we analyze one real data set.

In this paper, a modified form of the traditional inverse Lomax distribution is proposed and its characteristics are studied. The new distribution which called modified logarithmic transformed inverse Lomax distribution is generated by adding a new shape parameter based on logarithmic transformed method. It contains two shape and one scale parameters and has different shapes of probability density and hazard rate functions. The new shape parameter increases the exibility of the statistical properties of the traditional inverse Lomax distribution including mean, variance, skewness and kurtosis. The moments, entropies, order statistics and other properties are discussed. Six methods of estimation are considered to estimate the distribution parameters. To compare the performance of the different estimators, a simulation study is performed. To show the flexibility and applicability of the proposed distribution two real data sets to engineering and medical fields are analyzed. The simulation results and real data analysis showed that the Anderson-Darling estimates have the smallest mean square errors among all other estimates. Also, the analysis of the real data sets showed that the traditional inverse Lomax distribution and some of its generalizations have shortcomings in modeling engineering and medical data. Our proposed distribution overcomes this shortage and provides a good fit which makes it a suitable choice to model such data sets.

This study introduces a negative Rayleigh detection model for estimating population abundance in line transect surveys. The model satisfies key detection conditions and provides a detailed analysis of its probability density function, moments, and other essential characteristics. Parameters are estimated using three methods: moment estimator, maximum likelihood estimator, and Bayesian estimator. The model’s performance is evaluated through simulations, comparing its estimators to those from established models. An empirical application using perpendicular distance data further assesses the model, with goodness-of-fit statistics demonstrating its advantages over traditional methods.

In recent years, the Muth distribution has been used for the construction of accurate statistical models, with applications in various applied fields. In this paper, we use a truncated-composed scheme to create a new unit Muth distribution, from which we motivate a more general family of continuous distributions called the truncated Muth generated family. The key benefits of this family are its analytical simplicity, connections with the exponential generated family, and flexibility conferred on any parental distribution. In particular, it improves the capability of the functions of the parental distribution, enhancing their peak, asymmetry, tail, and flatness levels, among others. The characteristics of quantile and moment measures and functions of the truncated Muth generated family are described in detail. As a concrete example, a particular distribution that extends the Weibull distribution is highlighted. In an applied part, the parameters are calculated using the maximum likelihood procedure. We use a comprehensive simulation analysis to demonstrate the accuracy of the derived estimates. The revised Weibull model is then used to fit two real-world datasets. The new model is shown to be more suited to these datasets than other competing models.

Background Prediction models have gained immense importance in various fields for decision-making purposes. In the context of tennis, relying solely on the probability of winning a single match may not be sufficient for predicting a player's future performance or ranking. The performance of a tennis player is influenced by the timing of their matches throughout the year, necessitating the incorporation of time as a crucial factor. This study aims to focus on prediction models for performance indicators that can assist both tennis players and sports analysts in forecasting player standings in future matches. Methodology To predict player performance, this study employs a dynamic technique that analyzes the structure of performance using both linear and nonlinear time series models. A novel approach has been taken, comparing the performance of the non-linear Neural Network Auto-Regressive (NNAR) model with conventional stochastic linear and nonlinear models such as Auto-Regressive Integrated Moving Average (ARIMA), Exponential Smoothing (ETS), and TBATS (Trigonometric Seasonal Decomposition Time Series). Results The study finds that the NNAR model outperforms all other competing models based on lower values of Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). This superiority in performance metrics suggests that the NNAR model is the most appropriate approach for predicting player performance in tennis. Additionally, the prediction results obtained from the NNAR model demonstrate narrow 95% Confidence Intervals, indicating higher accuracy and reliability in the forecasts. Conclusion In conclusion, this study highlights the significance of incorporating time as a factor when predicting player performance in tennis. It emphasizes the potential benefits of using the NNAR model for forecasting future player standings in matches. The findings suggest that the NNAR model is a recommended approach compared to conventional models like ARIMA, ETS, and TBATS. By considering time as a crucial factor and employing the NNAR model, both tennis players and sports analysts can make more accurate predictions about player performance.

In this study, we suggested an innovative approach by introducing an Adaptive Exponential Weighted Moving Average (AEWMA) control chart utilizing Variable Sample Size (VSS) under Bayesian methodology. The proposed methodology utilized an integer linear function to dynamically adjust sample sizes according to the AEWMA statistic. Another appealing feature of our adaptive framework is the integration of the smoothing constant of an EWMA chart, which enhances monitoring responsiveness. We reveal the superiority of our recommended control chart by extensive simulations to existing Bayesian EWMA and Bayesian AEWMA control charts using Fixed sample size (FSS). The offered Bayesian VAEWMA control chart is more sensitive to detection improvement, a decrease in the false alarm rate, and overall more effective than the existing methods. These findings provide additional justification for the basic notion that process control statistical tools needed to be dynamic, as the manufacturing process itself was dynamic. The results suggest the importance of introducing adaptive SPC methods in dynamic manufacturing environments. A real data application is performed to evaluate the validity and optimal performance of our recommended chart.

In this paper, we propose a new extension of the traditional Rayleigh distribution called the modified Kies Rayleigh distribution. The new distribution contains one scale and one shape parameter and its hazard rate function can be increasing and bathtub-shaped. Some mathematical properties of the new distribution are derived including quantiles and moments. The parameters of modified Kies Rayleigh distribution are estimated based on progressively Type-II censored data. For this purpose, we consider two estimation methods, namely maximum likelihood and maximum product of spacing estimation methods. To compare the efficiency of the proposed estimators, a simulation study is carried out. To show the applicability of the new model as well as the estimation methods, one real data for failure times of software is analyzed. Based on the empirical parts, we can conclude that the proposed model can be considered as a good model in the field of life testing and reliability analysis compared with other competing models.

In this paper, we present a new family of continuous distributions known as the type I half logistic Burr X-G. The proposed family’s essential mathematical properties, such as quantile function (QuFu), moments (Mo), incomplete moments (InMo), mean deviation (MeD), Lorenz (Lo) and Bonferroni (Bo) curves, and entropy (En), are provided. Special models of the family are presented, including type I half logistic Burr X-Lomax, type I half logistic Burr X-Rayleigh, and type I half logistic Burr X-exponential. The maximum likelihood (MLL) and Bayesian techniques are utilized to produce parameter estimators for the recommended family using type II censored data. Monte Carlo simulation is used to evaluate the accuracy of estimates for one of the family’s special models. The COVID-19 real datasets from Italy, Canada, and Belgium are analysed to demonstrate the significance and flexibility of some new distributions from the family.