The practice of incorporating extra parameters into standard models is a common technique in statistical analysis. Adding an extra parameter enables the formation of a new model by applying the modified alpha-power transformation, employing the Nadarajah-Haghighi model as the baseline. Numerous characteristics of the said model are acquired, like the mode, quantiles, entropies, stochastic orders, mean residual life function, and order statistics. The maximum likelihood estimation method has been employed to estimate the parameters of the suggested model. To show how well the suggested distributions will function in a real-world setting, a simulation study has also been carried out and data has been examined. It is attained that the proposed model outperforms several other cutting-edge, current models as well as the baseline.

Statistical methodologies play a crucial role in biomedical research, particularly in the analysis of clinical and survival data. In oncology, specialized statistical frameworks are often necessary to accurately characterize time-to-event outcomes. This study introduces a generalized model that yields a weighted probability distribution, specifically the Length-Biased Sujit (LBSJT) distribution, derived as an extension of the conventional Sujit model. The proposed distribution incorporates a length-biased mechanism, enhancing its flexibility for modeling survival times. A comparative analysis is conducted between the original and the length-biased versions to evaluate their respective fitting capabilities. Key theoretical properties of the LBSJT distribution are established, including raw moments, the moment generating function, and reliability-related measures. Additional analytical features such as the Bonferroni and Lorenz curves and incomplete moments are also derived. Parameter estimation is performed using the maximum likelihood approach, and a comprehensive Monte Carlo simulation is carried out to assess the precision and robustness of the estimators. The results demonstrate strong estimation accuracy, particularly with increasing sample size and parameter values. Finally, the applicability and effectiveness of the proposed distribution are demonstrated through its application to clinical remission data, where the LBSJT model provides a superior fit compared to several well-established distributions.

This paper proposes a novel one-parameter discrete probability model, termed the Poisson-Sujit (PSJT) model, developed by compounding the classical Poisson distribution with the recently introduced Sujit (SJT) model. The resulting model offers improved flexibility for modeling count data by leveraging the analytical simplicity of the Poisson framework and the adaptability of the SJT distribution. A comprehensive theoretical analysis establishes key distributional characteristics, illustrating that an increase in the model's parameter leads to reductions in the mean, variance, and IQR, while the skewness exhibits an increasing trend. Parameter estimation is carried out using both the method of moments and maximum likelihood estimation techniques. To evaluate the statistical properties of the estimators, an extensive Monte Carlo simulation study is performed, indicating that the maximum likelihood method consistently provides greater accuracy and efficiency across a range of scenarios. The practical relevance of the PSJT distribution is demonstrated through its application to two empirical datasets: one related to cytogenetic damage analysis, and another involving dicentric chromosome counts in human peripheral blood following exposure to a 1.600 Gy dose of 1480 MeV oxygen ions. Comparative goodness-of-fit assessments confirm the superior fitting capability and interpretability of the PSJT model relative to existing alternative distributions.

This paper proposes the Poisson-Emrem (PEm) distribution, a new one-parameter discrete probability model obtained by compounding the Poisson and Emrem distributions. The model preserves the mathematical tractability of the Poisson law while offering greater flexibility for analyzing count data in health and biological sciences. A theoretical study establishes its principal properties, showing that increases in the parameter lead to systematic reductions in the mean, variance, and interquartile range, with a corresponding increase in skewness. Additional features such as moments, dispersion index, and the hazard rate function are derived, the latter characterized by a bathtub-shaped form that is particularly suitable for lifetime studies. Parameters are estimated using maximum likelihood, and Monte Carlo simulations confirm the accuracy and efficiency of the estimator. The applicability of the PEm distribution is demonstrated through two empirical datasets involving cytogenetic abnormalities in rabbit lymphoid cells under streptogramin treatment and daily COVID-19 mortality counts in South Korea. Comparative goodness-of-fit analyses show that the proposed model consistently provides superior performance over competing discrete distributions. Owing to its ability to effectively capture skewness, over-dispersion, and zero inflation, the PEm distribution offers a flexible and reliable framework for modeling complex count data arising in health and biological sciences. These findings highlight its potential usefulness in public health monitoring and related statistical applications.

By incorporating the unit Gompertz (UG) distribution into the framework of artificial neural network (ANN) modelling, we present a novel approach in this paper. We include the UG distribution in our ANN modelling framework to improve the precision and interpretability of predictions. Through this integration, we hope to learn new things, strengthen forecast accuracy, and better understand the mechanisms at work in our data. After performing computations for a number of situations using the Hazard Rate Function (HRF), Cumulative Density Function (CDF), Probability Density Function (PDF), and Reliability (R) functions, a data collection has been developed. With this UG distribution and ANN modelling combo, it is expected that the ability to analyze and predict these functions would improve. Two separate artificial neural network models have been created using a total of 32 data sets gathered. The generated multi-layer perceptron network models utilized 15% for model validation, 70% of data for model training, and 15% for model testing. The findings demonstrate that ANNs are highly accurate at predicting the PDF, CDF, HRF, and R functions of the UG model.

This study primarily advances the theoretical development of the PoissonGarima (PSNG) distribution by establishing several novel properties not previously addressed in existing literature. These theoretical enrichments enhance the model’s statistical foundation and extend its applicability to overdispersed count data commonly observed in fields such as agriculture, biology, and medicine. As a secondary contribution, the improved PSNG model is applied to statistical process control through the development of PSNG-based control charts for monitoring count data. The proposed charts are evaluated via simulation studies and validated with an empirical agricultural dataset, where their performance is benchmarked against eight competing models. Additionally, comparisons between PSNG- and Poisson-based control charts demonstrate the superiority of the proposed approach in detecting process shifts under overdispersion. This integrated approach reinforces the PSNG distribution’s theoretical depth while demonstrating its practical relevance in quality monitoring contexts.

This study presents a numerical and statistical investigation of Casson magnetohydrodynamic (MHD) nanofluid flow with Marangoni convection over an inclined surface, incorporating several complex physical effects. The Casson fluid model accounts for shear-thinning behavior, while nanoparticle dynamics are captured through Buongiorno’s model, considering Brownian motion and thermophoresis. Additional phenomena such as thermal radiation, Joule heating, viscous dissipation, internal heat generation, and an Arrhenius-type chemical reaction with activation energy are also included. The governing nonlinear boundary layer equations, formulated via similarity transformations, are solved using the fourth-order Runge-Kutta methodology coupled with a shooting technique. To reinforce the numerical findings, statistical analysis is conducted through Pearson correlation coefficients and multiple linear regression. These techniques quantify the interrelationships among key dimensionless parameters and their influence on output quantities such as skin friction, Nusselt number, and Sherwood number. Diagnostic tools including residual plots, Q−Q plots, and leverage statistics are employed to verify model assumptions and assess statistical robustness. The results show that increasing magnetic field strength and Casson parameter suppresses fluid velocity due to enhanced resistive forces, while internal heat generation, radiation, and viscous dissipation significantly elevate the temperature field. Brownian motion and thermophoresis parameters are found to play opposing roles in nanoparticle concentration distribution. Weak multicollinearity among predictors also supports the stability of the regression models. This combined numerical statistical framework offers valuable insights into optimizing non-Newtonian nanofluid systems subjected to thermally and chemically complex conditions over inclined geometries.

This study introduces a novel one-parameter discrete probability distribution, the Poisson-Mgamma (PMga), constructed by compounding the classical Poisson distribution with the Mgamma distribution. The model combines enhanced flexibility for analyzing count data with the mathematical tractability of the Poisson framework. Theoretical analysis shows that as the model parameter increases, the mean, variance, and interquartile range decrease, while skewness increases. With closed-form moments and adaptable tail behavior, the PMga distribution serves as a simple yet powerful tool for modeling dispersion in count data. Parameter estimation is performed using the maximum likelihood estimation, with Monte Carlo simulation results indicating that MLE consistently yields greater accuracy and efficiency. The practical applicability of the PMga model is demonstrated through its analysis of two biologically significant datasets: dicentric chromosome counts in human peripheral blood following exposure to 1.600 Gy of 1480 MeV oxygen ion radiation, and yeast cell counts obtained via hemocytometer measurements. Comparative goodness-of-fit assessments indicate that the PMga distribution provides improved performance relative to several existing models, highlighting its potential as a versatile tool for modeling biological count data.

Probability-based methods play a crucial role in supporting decision-making under uncertainty. This study introduces a novel probabilistic framework designed to improve the modeling of complex healthcare data an essential step toward advancing medical research and optimizing clinical outcomes. Traditional statistical techniques often fall short when addressing the intricate nature of such data. To overcome these limitations, we propose an innovative approach based on the flexible Rayleigh-Weibull distribution. The model exhibits distinctive features and is accompanied by a robust parameter estimation procedure, validated through comprehensive simulation studies. Its effectiveness is further demonstrated through applications to real-world datasets, including pharmaceutical efficacy, survival times of bladder cancer patients, and outcomes for individuals undergoing chemotherapy. Rigorous data validation confirms the model’s reliability and accuracy. Statistical evaluations reveal that the proposed distribution offers superior adaptability and performance, establishing it as a compelling alternative to existing models in the analysis of lifetime data.

Modern technology development heavily relies on nanotechnology, which has gained significant attention from researchers in recent years, particularly in finding ways to enhance heat transfer rates. One approach to addressing this issue is to use nanoparticles in host fluids to greatly improve their thermal properties. This study employed response surface methods to investigate the Walter’s B nanofluid, incorporating thermophoresis, Brownian diffusion, activation energy, and thermal radiation, using the Buongiorno model to examine nanofluid properties. To reduce the formed system of flow equations into a dimensionless differential form system, appropriate variables were used. In addition, we build a dataset for the proposed multilayer perceptron neural network using the Runge-Kutta fourth-order shooting method. The study analyzed effects of flow variables on the velocity field, temperature field, and species volumetric concentration fields, and probable error correlation coefficients were calculated to evaluate the statistical significance of the parameters. Additionally, a sensitivity analysis was conducted, which showed that with a high thermophoresis number, the Nusselt number is more sensitive.

Statistical methods are crucial for making informed decisions under uncertainty. This study introduces a new probability model designed to improve data analysis in engineering, pharmaceutical sciences, and metrology. Traditional models often struggle with complex data patterns, so we propose a statistical framework based on the flexible Teissier distribution. The model's key properties are explored, and parameter estimation is carried out using reliable statistical techniques, supported by simulation studies. Real-world data from engineering, pharmaceutical, and metrological applications are used to assess the model's accuracy. Statistical tests confirm its consistency and precision. The entropy-transformed Teissier distribution shows strong adaptability, making it a practical and effective choice compared to existing methods.

In the realm of statistical mechanics, unit models are commonly employed to elucidate tangible numerical values that fall within the range of 0-1, encompassing entities like proportions, percentages, and probabilities. Unit models are frequently created by adapting an existing model originally defined in a broader domain, while others are explicitly formulated independently. This study aims to develop a novel unit interval lifespan model with a small number of parameters that is capable of describing more complex failure patterns, such as growing and bathtub-shaped failure rates. The unit Bilal (UB) model, based on the inverse-exponential technique and the Bilal model, is explained in this research study. Different statistical features and aspects of reliability are investigated. The results have both theoretical and practical implications. We derive explicit expressions for primary functions from the UB distribution from a theoretical perspective. To evaluate parameter, estimate approaches, we demonstrate various numerical and graphical simulation findings. The applicability of the model to real-world data is also discussed.

ABSTRACT Standard distributions must be improved to enhance their capacity for data modeling because they do not inherently suit all sorts of data sets in an acceptable manner. Due to this lack of previous ones, we developed a novel model employing the entropy‐transformed function. We utilized the inverse Weibull model to function as the reference model to assess the applicability of the entropy transformation. The distribution, referred to as the “Entropy‐Transformed Inverse Weibull Distribution” (ETIWL), is derived by applying the entropy transformation to the inverse Weibull model. The proposed distribution's core characteristics have been taken into account. The maximum‐likelihood approach is used to estimate the parameters of the given distribution. Four real data sets are used in this study with the thorough simulation analysis to see whether the proposed distribution is superior.

Due to the presence of alternate energy sources such as solar PV cell, wind, hydro etc. it is the ability of the power system to attain feasible operation and maintain the reliability of the system. These renewable energy sources provide many benefits with advanced technologies for overcoming pollution problems and maintenance costs. Since the energy demands increase then hybrid energy systems have been introduced for continuous power supply between the grid and consumer. These local non-conventional energy sources are properly used by using the concept of micro grid so this problem can be optimized even in remote area applications. Through such hybrid energy system, it provides improves reliability and power quality with better utilization efficiency. This paper emphasizes the interfacing of various energy sources to make hybrid power systems and simulation study for enhancing stability, power quality in order to optimize energy sources.

A thorough understanding of magnetohydrodynamic (MHD) squeezing fluid flow in non-Darcian media is essential for advancing a wide range of engineering applications, including cooling systems, polymer processing, and biomedical devices. This study investigates the dynamics of MHD squeezing flow over a stretching permeable plate, focusing on the combined effects of convection and nonlinear stratification on mass and heat transfer processes. The influence of thermal radiation is also considered to provide a comprehensive analysis of heat transfer mechanisms. The fourth-order Runge–Kutta method (RK-4), coupled with a shooting technique, is employed to numerically solve the system of nonlinear governing equations. The contribution of key variables to the flow field is studied and visualized through graphical representations. In addition, Sherwood number, Nusselt number, and skin friction coefficient are determined for various parameter values, with their statistical significance examined using correlation coefficients and probable error analysis. The results reveal that increasing solutal and thermal stratification parameters diminishes concentration and temperature fields, whereas higher Biot numbers enhance fluid concentration and temperature. Notably, all values are statistically significant except for length variable δ in the local Nusselt number.

The flow of a viscous fluid over a rotating frame is a characteristic phenomenon observed in numerous manufacturing processes, especially in structures featuring rotating disks. This paper examines the combined effects of Hall effect, thermal radiation and variable viscosity on the unsteady flow near a stagnation point over a rotating disk. The study examines the flow in two scenarios: tri-hybrid nanofluid flow and mono-nanofluid flow. Through suitable similarity transformations, the PDEs governing the flow problem are transformed into ODEs, which are then solved numerically using the “bvp4c” function in MATLAB. A validation of numerical code is done by a comparison with results from existing literature. The influence of key parameters on flow characteristics and the heat transfer rate are illustrated graphically. Subsequently, an advanced artificial neural network (ANN) is employed to predict the Nusselt number. The heat transfer rate exhibited by the THNF is marginally superior to that observed in the NF. The rate of entropy generation in the region near the disk is marginally greater for the THNF than for the NF. The HT rate values predicted by neural network show good accuracy which was assessed by mean squared error and regression coefficient. The findings of this study will benefit various fields involving rotating disk systems like brakes, gears, flywheels, gas turbine engines, geothermal extraction, rotor-stator systems, computer devices, etc.

Thermal energy is produced from sunlight through solar thermal collectors, with the parabolic trough solar collector (PTSC) playing a crucial role in concentrated solar power (CSP) technologies by capturing solar energy at temperatures between 325 and 700 K. The tangent hyperbolic fluid model, a non-Newtonian fluid model, effectively predicts shear thinning behavior, as shown in experimental studies. This model’s rheological properties at varying shear rates contribute to its superior heat transmission performance. This study investigates the thermal efficiency of Darcy–Forchheimer magnetohydrodynamic tangent hyperbolic fluid flow in inclined cylindrical films, incorporating a non-uniform heat source/sink in the PTSC framework. The analysis considers the effects of radiation alongside the non-uniform heat source or sink on thermal phenomena. By applying relevant transformations, the governing equations are reformulated into a nonlinear ordinary differential system, solved using the Runge–Kutta fourth-order method with the shooting technique. Results are analyzed mathematically and graphically. The correlation coefficient is used as a statistical metric to examine the relationship between key parameters and their effect on the skin friction coefficient (SKF) and local Nusselt number (LNN). This approach evaluates potential errors to determine statistical significance. Findings show that Reynolds number exhibits a strong correlation of 0.8828 with SKF and 0.9769 with LNN, suggesting significant effects on heat transfer. Notably, parameters such as local porosity number and magnetic number affect SKF, while local porosity and mixed convection parameters strongly correlate with LNN, indicating that utilizing such fluids in PTSCs can enhance heat transmission rates and optimize solar energy utilization, ultimately improving system efficiency.

Statistical process control (SPC) is vital for overseeing processes and ensuring quality standards, with control charts being key tools in this process. As manufacturing systems and components become more complex, there is an increasing demand for control charts built on advanced statistical distributions. The Poisson-based count chart is commonly used to monitor nonconformities in production, but its use depends on the assumption that the mean and variance of the data are equal. In many cases, particularly in fields such as biology and medicine, overdispersion occurs, where the variance surpasses the mean. In such cases, the Poisson Chris-Jerry (PSNCJ) distribution offers a more suitable approach for modeling count data. This study explores the development and characteristics of the PSNCJ distribution and presents control charts specifically designed for datasets that conform to this model. Its effectiveness is evaluated through both simulations and real-world applications. Moreover, the PSNCJ count chart is applied to datasets from agriculture and biology, demonstrating its practical significance in these fields. The results validate the utility and accuracy of the proposed control charts.

This study presents a four-parameter distribution which is called the Harris generalized Kappa distribution, which is flexible and tractable. The new distribution extends the two-parameter Kappa distribution, and it can be explored to model highly skewed data, especially those exhibiting decreasing, increasing, reversed J, and non-monotone (bathtub) failure rates. Mathematical expressions were derived for the statistical properties of the Harris generalized Kappa distribution and studied in detail, namely: moments, incomplete moments, moment generating functions, characteristic function, mean residual life, average waiting time, Bonferroni and Lorenz curves, Gini index, Renyi and q-entropies, and stress-strength reliability function. The estimate of the parameters of the proposed model is obtained using the maximum likelihood estimation procedure with the adequacy model in R. The application of the Harris generalized Kappa model to two lifetime data sets, namely the taxes revenue's data and the fracture toughness data sets, demonstrated its applicability in modeling real-life data, as it provides the best fit among other competitive models considered in the study.

A novel two-parameter continuous model titled the entropy-transformed Gompertz (ETGPZ) distribution has been developed via the entropy transform. A new framework has been investigated and found to meet the criteria of the probability function. By significantly improving the functional shape and having the ability to model the most likely form of the hazard rate function, this new modification has increased the adaptability of the typical distribution. Some of its core characteristics, such as its statistical and computational features, are clearly presented. A thorough simulation analysis has been done to examine the final behavior of maximum likelihood estimators while estimating model parameters. We assess the performance and practical applicability of the ETGPZ distribution using eight real datasets from engineering and biomedical fields. The results demonstrate that the ETGPZ outperforms the baseline Gompertz (GPZ) distribution, highlighting its superiority and broader potential for various applications.