The Modern Journal of Statistics (MJS) is a leading international, peer-reviewed, open-access journal dedicated to advancing statistical science. Published biannually in July and January by Sphinx Scientific Press, MJS employs a rigorous double-blind peer-review process to ensure the highest academic standards. The journal emphasizes cutting-edge methodological and theoretical contributions in statistics, probability, and stochastic processes, as well as innovative applications across diverse scientific disciplines. These include, but are not limited to, biological and biomedical sciences, medicine, business, economics, social sciences, physics, data science, and engineering. By fostering the dissemination of high-quality research, MJS serves as a vital platform for statisticians, researchers, and practitioners worldwide, promoting interdisciplinary collaboration and the development of novel statistical methodologies. ISSN: 3068-8140
Double Transformation Sin-Exponential Distribution for Modeling Lifetime Data
This paper presents a new approach known as double transformation sine-exponential distribution (DT-Sin-E), a multi-processed distribution derived from two-stage transformation of the exponential baseline within a sine-generated context to improve the flexibility of the lifetime and reliability data analysis. Validation of this model proposed was confirmed and the main mathematical features such as the cumulative distribution function, probability density function, survival function, hazard rate function, cumulative hazard function, moments, quantile function, and random generation method were formulated. Eight parameter estimation strategies: maximum likelihood, least squares, weighted least squares, Cramér–von Mises, Anderson–Darling, maximum product of spacings, percentile estimation, and quasi-least squares were used. The Monte Carlo statistical analysis revealed that estimation accuracy increases with increasing size of the sample, but the best method depends on the sample size and the criterion of performance. Regarding the application in the real data field failure-time observations, the proposed model proved to be better than many established competing distributions on information criterion according to the goodness-of-fit measures and the graphical data analysis. These results suggest the DT-Sin-E distribution is an adaptable, efficient model on life data with complex behavior. The revised theoretical development further establishes stochastic ordering, scale behavior, mean residual life, order-statistic distributions, reliability measures, and Rényi and Shannon entropy representations.
Copyright (c) 2026 Khnsaa F. Hameed‏ Alazawey, Nihad Jalal Kadhim, Ahmed M. Azeez https://creativecommons.org/licenses/by/4.0
A New Logarithmic Pie Power-G family of Distributions: Properties and Applications to Medical and Traffic Data
The present study proposes a new versatile family of distributions, called the New Logarithmic Pie Power-G (NLPP-G) family of probability distributions, applying the Power transformation approach. The newly introduced family of distributions has the ability to enhance the flexibility level of the classical distributions without adding extra parameters. A special subcase of the NLPP-G family, by applying the Inverse Weibull model as a baseline member, is suggested. The subcase of the NLPP-G family is called the New Logarithmic Pie Power Inverse Weibull distribution (NLPP-IWD). The cumulative distribution, survival, probability density, and hazard functions of the NLPP-IWD are investigated graphically. Similarly, for the NLPP-IWD, various range of statistical properties, including moments, moment-generating functions, characteristic functions, incomplete moments, mean residual-life, and order statistics, are derived. Based on the Maximum Likelihood Estimation (MLE) method, we have estimated the unknown parameters of the NLPP-IWD, and its practical performance is verified by the Monte Carlo simulation analysis. The numerical results and graphical illustration of the Monte Carlo simulation analysis indicated that biases and mean square error decreased as the sample size increased. Lastly, three are considered to illustrate the practical effectiveness of the NLPP-IWD. The practical performance of the NLPP-IWD is compared with ten well-known distributions using different model selection measures. These evaluations provide empirical evidence that the introduced distribution performs better than ten well-known competing distributions.
Copyright (c) 2026 Zubir Shah, Zubair Ahmad, Zahra Almaspoor, Faridoon Khan, Chrisogonus K. Onyekwere, Gadde Srinivasa Rao, Saima K‎. ‎Khosa https://creativecommons.org/licenses/by/4.0
Designing of Multiple Dependent State Sampling Plan for Inverted Nadarajah-Haghighi distribution
A novel approach to quality control is proposed through the development of a multiple dependent state (MDS) sampling plan for time-truncated life tests. The proposed plan assumes that product lifetimes follow an inverted Nadarajah–Haghighi (INH) distribution, with product quality evaluated using a specified percentile lifetime. The sampling plan parameters, namely the sample size, acceptance and rejection numbers and the required number of preceding lots for decision-making are determined using a two-point approach based on the operating characteristic (OC) curve. Extensive tables are constructed for different values of the shape parameter, and the performance of the plan is thoroughly analyzed. The practical applicability of the proposed sampling scheme is illustrated using real-world data and its efficiency is compared with existing sampling plans. The results demonstrate that the proposed plan provides improved protection for both producers and consumers.
Inverted Nadarajah-Haghighi distribution
Copyright (c) 2026 Sd. Jilani, Srinivasa Rao Gadde https://creativecommons.org/licenses/by/4.0
Topp-Leone Reduced Kies Distribution for Unit-Interval Data: Statistical Properties, Parameter Estimation, and Applications
This study introduces a two-parameter lifetime model named the Topp-Leone Reduced Kies (TLRK) distribution, which extends the Topp-Leone-G family by incorporating the Reduced Kies (RK) distribution as its baseline. The proposed distribution is designed for unit-interval data, such as proportions, rates, and reliability metrics. The TLRK distribution exhibits left-skewed, right-skewed, decreasing (or L-shaped), bathtub-shaped, and near-symmetric shaped density while the hazard rate function exhibits an increasing, and bathtub-shaped failure rates behaviour. Several statistical properties of the TLRK distribution, including moments, moment generating function, Rényi entropy, and order statistics are investigated. Seven distinct parameter estimation methods namely maximum likelihood, least squares, Cramér-von Mises, maximum product of spacings, Anderson-Darling, weighted least squares, and percentile-based estimation; are implemented and compared. A Monte Carlo simulation study evaluates the finite-sample performance of these estimators across varying sample sizes. The practical utility of the TLRK distribution is demonstrated through the analysis of two real unit-interval datasets (failure times of Kevlar strands and relief times of arthritic patients). Comparative analysis indicates that the TLRK distribution shows a favourable fit relative to some existing RK-based models, including the Reduced Kies, Extended Reduced Kies, Exponential Reduced Kies, and Marshall-Olkin Reduced Kies distributions.
Copyright (c) 2026 Ehinomen Emmanuel Ehizojie https://creativecommons.org/licenses/by/4.0
Study Relative Loss Values ​​for Entropy Functions of Lindley and Truncated Lindley Distributions
Entropy is a measure of uncertainty in probability distributions when studying different phenomena. Numerical comparisons of the relative loss in entropy are calculated to determine which entropy measure has better advantages over the other. In this paper, five entropy measures are derived for the Lindley and truncated Lindley distributions to calculate the relative loss of entropy of the two distributions when the underlying probability distribution is the truncated Lindley distribution instead of the Lindley distribution, and to determine the best uncertainty measure based on the relative loss results.
Copyright (c) 2026 khalaf H. Al-Habib, Moudher Kh. Abdal-hammed, Ahmed M. Salih, Mundher A. Khaleel https://creativecommons.org/licenses/by/4.0
A Novel Flexible Logarithmic Cosine-G Family of Distributions with Applications to Event Time Data
Many probability distributions have been developed in the literature on distribution theory to describe and forecast real-world phenomena, especially in the domains of engineering, sports, and medicine. To give the current distribution greater flexibility, these distributions are generated with the addition of one or more extra parameters. Reparameterization and estimation issues are the two major issues that arise when additional parameters are added to the existing distribution. We make a significant attempt to propose a novel statistical methodological strategy for generating more flexible distributions devoid of extra parameters to prevent the aforementioned two issues. The logarithmic and cosine functions are used to build the recently described approach. A Novel Flexible Logarithmic Cosine-G (NFLC-G) family of distributions is the name given to the newly suggested approach. Additionally, some distributional characteristics of the NFLC-G family are also obtained. Using the newly suggested approach, a unique sub-model known as the Novel Flexible Logarithmic Cosine Weibull (NFLC-Wei) distribution is established. The Maximum Likelihood estimation method is used to estimate the model parameters of the proposed family of distributions. Similarly, a comprehensive Monte Carlo simulation analysis verifies the accuracy of the parameter estimation technique. From simulation analysis, it is observed that as the sample size increases, the biases and mean square errors declined as well as MLEs gradually approach the true parameter values. Moreover, three sets of biomedical data are demonstrated to check the applicability of the NFLC-G family of distributions. Using statistical information criteria, the performance of the proposed distribution is compared to other well-known existing distributions. Finally, we found that the NFLC-Wei distribution appears to be the best option for the studied data sets based on these statistical information requirements.
Copyright (c) 2026 Dr. Zubir Shah, Zubair Ahmad, Dr. Zahra Almaspoor, Dr. Faridoon Khan, Dr. Chrisogonus K. Onyekwere, Dr. Gadde Srinivasa Rao, Dr. Saima K‎. ‎Khosa https://creativecommons.org/licenses/by/4.0
Novel DUS Topp-Leone Burr-Hatke exponential model with properties and application to COVID-19 datasets
This study presents the DUSTopp-Leone Burr-Hatke-Exponential (DUSTLBHE) model, a new and more flexible extension of the BHE model. The DUSTLBHE model accommodates diverse density shapes such as right-skewed, heavy-tailed, unimodal, or decreasing, and failure rate patterns such as increasing, decreasing, inverted-bathtub, and reversed-J. Several statistical properties, including raw and incomplete moments, quantile and moment-generating functions, entropies, and order statistics, are derived and illustrated. The DUSTLBHE model parameters are estimated using the maximum likelihood estimation (MLE) method. Simulation studies were utilized to assess the accuracy and efficiency of the MLE, while three real datasets from medical and engineering applications demonstrate the model’s flexibility. The DUSTLBHE model is compared with several competing distributions using standard goodness-of-fit criteria such as the log-likelihood, Akaike information criterion (AIC), Bayesian information criterion (BIC), corrected AIC (AICc), Hannan Quinn IC (HQIC), and Kolmogorov–Smirnov (KVS) statistics. The results show that the DUSTLBHE distribution provides smaller AIC, BIC, AICc, HQIC, and KVS values and higher log-likelihood values than the competing models, indicating a superior fit to the datasets. These findings demonstrate that the DUSTLBHE model is a flexible and useful alternative for modelling skewed and heavy-tailed real-world data, particularly in epidemiological and reliability studies.
Copyright (c) 2026 U. F. Abbas, O. D. Adubisi https://creativecommons.org/licenses/by/4.0
Limit-Cycle Behavior of the Exponentiated Exponential Autoregressive Model: Theory and Applications
This study aims to design and evaluate a special nonlinear time series model, namely the exponentiated exponential autoregressive (EEAR) model, used to construct time series estimates that incorporate the cumulative distribution function of the raised exponential distribution. The underlying analytical constraints on the stability of these models and their limit cycles were obtained via local linearization techniques. The resulting models were developed by applying them to real data (monthly average of British pounds (in millions) spent by foreign visitors in the United Kingdom for the period 1-1-1988 to 31-12-2018) and indicated how efficiently they can capture the intricate dynamic character of data. The EEAR model was the best model according to information criteria, fit quality, and dynamically stable with respect to the different types of ordered models. The study represents a substantial improvement to the nonlinear time series model's theory, as well as new analytical resources to model complex economic and financial phenomena.
Copyright (c) 2026 Khitam M. Shakir, Hiba H. Abdullah https://creativecommons.org/licenses/by/4.0
A New Extended Fréchet Distribution: Properties, Characterizations, Modeling, and Risk Analysis for Medical Data
Measures like Value-at-Risk (VaR), Tail Value-at-Risk (TVaR), Mean-of-Order-P (MOO-P), and Peaks Over a Random Threshold VaR (PORT-VaR) are important in risk analysis, particularly when it comes to medical data. In order to better capture extreme occurrences in medical applications, this work presents the Extended Rayleigh-Fréchet (ER-Fr) model, a novel extreme value distribution. We derive and discuss several of their key mathematical and statistical properties that are particularly useful for risk assessment. A comprehensive simulation study is conducted to evaluate the performance of the maximum likelihood estimators under various sample sizes, confirming the model’s reliability. The practical utility of the ER-Fr distribution is demonstrated through the analysis of two real medical datasets: one on relief times for arthritic patients and another on survival times of guinea pigs exposed to tuberculosis. The model is compared with several existing Fréchet-type distributions using standard goodness-of-fit criteria, and it consistently outperforms its competitors. Based on this analysis, we provide actionable insights and recommendations for healthcare practitioners and risk analysts. The results highlight the ER-Fr model as a powerful and flexible tool for modeling extreme values and assessing risk in medical studies.
Copyright (c) 2026 Haitham M. Yousof, G.G. Hamedani, M. Masoom Ali, Magdy Tork, Manal A. Abdelrahaman, Mohammed R. Alzahrani, Hassan Alsuhabi, Abdirashid M. Yousuf, Abdisalam Hassan Muse https://creativecommons.org/licenses/by/4.0
An Analysis of the Relationship Between Production, Sales, and Export in the Indian Automobile Industry: Using Time Series
This study examines how production, sales, and exports are related in the Indian auto industry using data from 1994 to 2023. The Augmented Dickey-Fuller (ADF) tests show that all the variables are not stationary at levels, but they do become stationary after the first difference. A Vector Auto Regression (VAR) model used to the differenced log-transformed data shows that variations in production considerably and positively affect exports at the 10% level, showing the importance of supply-side capacity in increasing international competitiveness. Sales, on the other hand, have no direct effect on exports, which highlights that domestic demand is not affected by external performance. These findings show that capacity of production, rather than sales expansion, is the primary factor influencing vehicle export trajectory of India, offering guidance for industry strategy and formulation of policy.
Copyright (c) 2026 Jyoti Yadav, Anu, Chitra Kumari https://creativecommons.org/licenses/by/4.0
A Novel Alpha Power Gumbel-X Family of Distributions with Exponential Baseline
This study introduces the Novel Alpha Power Gumbel-X (NAPG-X) family of distributions, developed through the T-X transformation with a logarithmic generalizer. The NAPG-Exponential (NAPGEX) distribution is studied as a sub-model, with key mathematical properties derived, including the probability density function, cumulative distribution function, moments, moment generating function, Rényi entropy, and order statistics. The hazard rate function exhibits versatile shapes including increasing-decreasing, reversed-J, and L-shaped, making it suitable for diverse reliability applications. Ten classical estimation methods are evaluated through extensive Monte Carlo simulations across varying sample sizes and three parameter combinations. Results demonstrate that maximum likelihood and Anderson-Darling consistently provide superior performance with minimal bias, mean relative errors and root mean square errors. Furthermore, the practical applicability of the NAPGEX distribution is validated using three real-life datasets. Comprehensive comparisons using various performance measures reveal that the NAPGEX significantly outperforms competing models. These findings establish the NAPG-X family as a flexible and powerful tool for modeling asymmetric, positively skewed lifetime datasets across several scientific disciplines.
Copyright (c) 2026 Israel P. Reuben, Adubisi D. Obinna, David I. John, Bako B. Bitrus https://creativecommons.org/licenses/by/4.0
Comparison of Machine Learning Algorithms for Flood Prediction in Puri, Odisha
Floods pose a serious risk to communities, infrastructure, and overall regional development. Puri, a district in Odisha, India, is particularly prone to flooding due to its low-lying landscape and the heavy rains that occur during the monsoon season. In such areas, quick and accurate flood forecasting becomes crucial for protecting lives, planning evacuations, and reducing damage. This study aims to compare numerous machine learning methods, including Decision Trees, Logistic Regression, Random Forests, Support Vector Machines (SVM), and Lasso Regression, for predicting possible flood events using past flood data and environmental factors like rainfall, soil moisture, temperature, and other hydrological indicators. Soil moisture is an important variable, but its dataset was incomplete. To fill these gaps, three machine learning models were tested for soil moisture prediction. Lasso Regression performed the best, giving the lowest Mean Absolute Percentage Error (MAPE) of 0.17, and was chosen to generate the missing values. With this completed dataset, multiple algorithms were evaluated for flood prediction. Logistic Regression stood out, achieving a Recall Score of 1, a Matthews Correlation Coefficient (MCC) of 0.68, and an accuracy of 0.91. These results show that Logistic Regression is a strong and reliable choice for predicting floods in the Puri region.
Copyright (c) 2026 Rinku Poonia, Ravinder Singh, R.K. Bhardwaj, Vikas Kumar, Aarzoo Rani https://creativecommons.org/licenses/by/4.0
Modi linear failure rate distribution with application to survival time data
A new lifetime model, named the Modi linear failure rate distribution, is suggested. This flexible model is capable of accommodating a wide range of hazard rate shapes, including decreasing, increasing, bathtub, upside-down bathtub, and modified bathtub forms, making it particularly suitable for modeling diverse survival and reliability data. Our proposed model contains the Modi exponential distribution and the Modi Rayleigh distribution as sub-models. Numerous mathematical and reliability properties are derived, including the $r^{th}$ moment, moment generating function, rth conditional moment, quantile function, order statistics, mean deviations, Rényi entropy, and reliability function. The method of maximum likelihood is employed to estimate the model parameters. Monte Carlo simulations are presented to examine how these estimators perform. The superior fit of our newly introduced model is proven through two real-world survival data sets.
Copyright (c) 2026 Lazhar Benkhelifa https://creativecommons.org/licenses/by/4.0
A New Modification for the Inverse Rayleigh Distribution with Properties, Entropy Information, and Applications to Environmental Data
In the present study, we develop a new version of the inverse Rayleigh model using the odd-type G family of distributions. The proposed model is highly flexible and exhibits various behaviors in terms of its density and hazard functions. We study the mathematical properties of this new model, such as moments, quantile function, moment generating function, skewness, kurtosis, and entropy measures. The unknown parameters of the proposed distribution are estimated using the well-known maximum-likelihood method. A simulation experiment is evaluated to assess the effectiveness of the applied estimation method. Finally, the superiority and flexibility of the newly presented distribution are examined by analyzing two real data sets. The application of the proposed model is compared with other existing probability distributions, and based on specific evaluation criteria, we observe that the proposed distribution offers optimal fitting compared to other rival distributions.
Copyright (c) 2026 I. Elbatal, Ehab M. Almetwally, Mohammed Amine Meraou, Samirah Alzubaidi, M. H. Harpy, Elkhateeb S Aly, Rahmtalla Y. Yagoub, Abdisalan Ahmed Osman https://creativecommons.org/licenses/by/4.0
Obulezi distribution: a novel one-parameter distribution for lifetime data modeling
This paper introduces the novel, single-parameter Obulezi distribution for modeling lifetime data. We derived its statistical and reliability properties and performed an exhaustive comparison of fifteen parameter estimation techniques via simulation and application to three real datasets. Simulation results confirmed the consistency of all estimators, while empirical analysis showed the Obulezi distribution consistently yielded the lowest standard errors, proving it to be the most precise and stable model compared to competitors. Goodness-of-fit metrics confirmed the \texttt{Obulezi} distribution's superior fit, particularly for data exhibiting an increasing hazard rate. The Obulezi distribution is thus a robust and highly competitive model for parsimonious survival and reliability analysis.
Copyright (c) 2026 Okechukwu Obulezi https://creativecommons.org/licenses/by/4.0
The Neutrosophic Gompertz-G Family: Analytical Properties, Simulation Studies, and Applications to Real Data
This research deals with finding a family of continuous distributions according to neutrosophic logic called neutrosophic Gompertz-G (NGo-G), where the Gompertz family is obtained according to the T-X method and then merging the family using the direct method of neutrosophic logic to obtain it. The study also provides a detailed analysis of the statistical characteristics of the family of distributions, then using the exponential distribution according to this family to obtain a new distribution consisting of three neutrosophic parameters and neutrosophic variable called a neutrosophic Gompertz exponential (NGoE), in addition to reviewing the basic characteristics of NGoE, and providing a comprehensive analysis of the characteristics of the new distribution and estimate its parameters. In addition, a Monte Carlo simulation of the new distribution is carried out in order to validate its characteristics and guarantee that it is accurate prior to the implementation of our suggested model estimator. In addition, the distribution is applied to two different kinds of real data, and then the results of the new distribution are compared with the results of other distributions using two different informatics standards. This is done in order to determine the effectiveness of the distribution in modeling, as well as to demonstrate that it is superior to well-known models from the literature when it comes to fitting these real data sets.
Neutrosophic logic; Gompertz-G family; exponential.
Copyright (c) 2026 Nooruldeen A. Noori, Mundher A. Khaleel, Tumadher M. Alharigy, Ehab M. Almetwally, Mohammed Elgarhy https://creativecommons.org/licenses/by/4.0
A New Modified Arctan Model: Statistical Properties, Estimation Methods, Simulation Study, and Real-Life Application
This study introduces the modified Weibull Arctan (MWArctan) distribution, a new model derived from the Modified Weibull-G (MWG) family using the Arctan function as a generator. The theoretical formulation of the distribution is presented through derivations of its probability density function, cumulative distribution function, survival function, and hazard function. Analytical expansions are developed to simplify the computation of statistical properties, moments, and the quantile function. Three parameter estimation methods were evaluated through a Monte Carlo simulation across various sample sizes. The MLE method consistently produced the most efficient and stable estimates, exhibiting the lowest bias, MSE, and RMSE values. In contrast, LSE demonstrated lower bias only for small samples, but higher variance. The practical applicability of the MWArctan model was verified using real-life data from 40 turbochargers in diesel engines. The proposed model achieved the best fit compared to six competing Arctan-based distributions, as indicated by specific information criteria and goodness-of-fit tests. Graphical comparisons confirmed its superior flexibility in capturing both the central tendency and tail behavior of the empirical data. These results establish MWArctan as a robust and adaptable model for analyzing reliability and lifetime data.
Copyright (c) 2026 Ahmed M. Gemeay, Nooruldeen Ayad Noori, Khder Alakkari, Mundher A. Khaleel, Faisal A. M. Ali, Gizachew Tirite Gellow, Alexis Habineza, Ali T. Hammad https://creativecommons.org/licenses/by/4.0
A New Transformation to Reduce Skewness in Data with Bounded Support
Normality is a critical assumption for many statistical analyses, yet real-world data often deviate from this requirement. To address this, statisticians may employ robust methods or apply transformations to achieve approximate normality. This study proposes a novel transformation for data from bounded-support distributions, such as the beta family, to induce symmetry or near-symmetry. The method utilizes a data-driven parameter, estimated through a simple and efficient procedure. Examples demonstrate the transformation's effectiveness, and its straightforward implementation allows easy reversion to the original data scale. We recommend this approach for statistical analyses requiring normality, even for datasets that are approximately normal, due to their versatility and robustness.
Normal distribution, Transformation, Symmetry, Simulation
Copyright (c) 2026 Mahmoud A. Eltehiwy, Noura A. Taha AbuEl-magd https://creativecommons.org/licenses/by/4.0
Inference under hybrid censoring for the quadratic hazard rate model: Simulation and applications to COVID-19 mortality
This study implements Bayesian along with non-Bayesian approaches to estimate the parameters of the three-parameter quadratic hazard rate distribution using hybrid Type-II censoring. The model expands upon linear hazard rate, exponential, and Rayleigh distributions. In the non-Bayesian framework, point estimates and survival and hazard functions are calculated using maximum likelihood estimation (MLE). Asymptotic confidence intervals are derived, with a focus on the delta method. By applying independent normal and gamma priors, Bayesian inference produces point estimates and credible intervals using different symmetric and asymmetric loss functions. The analytical intractability of posterior distributions makes Markov chain Monte Carlo (MCMC) methods necessary for sampling purposes. The evaluation of point and interval estimates depends on root mean squared error (RMSE) in combination with mean relative absolute bias (MRAB), average confidence interval length (AL), and coverage probability (CP). The performance evaluation through different sample sizes and censoring schemes is conducted by simulation studies, while real-world data from COVID-19 mortality demonstrates the practical implementation of methods. Graphical and numerical analyses confirm the existence and uniqueness of the estimates. Results indicate that Bayesian methods deliver superior accuracy and more robust estimates than their non-Bayesian counterparts for survival analysis purposes in clinical and medical research.
Copyright (c) 2026 Moustafa N. Mousa, M. E. Moshref, N. Youns, M. M. M. Mansour https://creativecommons.org/licenses/by/4.0
Development and Applications of a New Hybrid Weibull-Inverse Weibull Distribution
This study introduces and applies a novel statistical model known as the hybrid Weibull inverse Weibull (HWIW) distribution, which combines the characteristics of the Weibull and inverse Weibull distributions to provide a more flexible model for representing real-world data, especially those characterized by asymmetry or extreme values. The basic functions of the distribution were derived, along with other statistical measures such as moments, the quantile function, and entropy were also derived. The distribution parameters were estimated using three distinct approaches, and their performance was evaluated through a Monte Carlo simulation to assess the performance and precision of each estimation technique. The results were used to show the most accurate estimation method for different samples. The proposed model was utilized to test two practical datasets; the findings demonstrated that the HWIW distribution outperformed six competing IW distributions in terms of model selection metrics. These results confirm the efficiency of the HWIW model’s ability to capture the structure of complex datasets and open the way for its use in multiple applications, including medical, industrial, and social fields, with the potential to be expanded to include multidimensional data or integrated with artificial intelligence techniques.
Copyright (c) 2025 Nooruldeen A. Noori, Kamal Najim Abdullah, Mundher A. khaleel https://creativecommons.org/licenses/by/4.0
New Modified Liu Estimators to Handle the Multicollinearity in the Beta Regression Model: Simulation and Applications
The beta regression model (BRM) is widely used for analyzing bounded response variables, such as proportions, percentages. However, when multicollinearity exists among explanatory variables, the conventional maximum likelihood estimator (MLE) becomes unstable and inefficient. To address this issue, we propose new modified Liu estimators for the BRM, designed to enhance estimation accuracy in the presence of high multicollinearity among predictors. The proposed estimators extend the traditional Liu estimator by incorporating flexible biasing parameters, offering a more robust alternative to the MLE. Theoretical comparisons demonstrate the superiority of the new estimators over existing methods. Additionally, Monte Carlo simulations and real-world applications evidence their improved performance in terms of mean squared error (MSE) and mean absolute error (MAE). The results indicate that the proposed estimators significantly reduce estimation bias and variance under multicollinearity, providing more reliable regression coefficients.
Copyright (c) 2025 Ali T. Hammad, Eslam H. Hafez, Usman Shahzad, Elif Yıldırım, Ehab M. Almetwally, B. M. Golam Kibria https://creativecommons.org/licenses/by/4.0
Fundamental Properties of the Characteristic Function using the Compound Poisson Distribution as the Sum of the Gamma Model
Probability distribution has proven its usefulness in almost every discipline of human endeavor. For this, the zero-truncated Poisson gamma (ZTP-G) model is widely recognized in probability theory and extensively used in various applied fields, specifically in survival, hydrology, insurance, and energy theory. The characterization of the zero-truncated Poisson sum of independent and identically distributed gamma random variables is proposed in this paper by applying the Laplace-Stieltjes transform technique. Further, the properties of continuity and quadratic form of the characteristic function are applied for definite positive properties from the ZTP-G model.
Copyright (c) 2025 Meraou M. A., Noriah M. Al-Kandari, Raqab Z. Mohammad https://creativecommons.org/licenses/by/4.0
Fitting Real Data Sets by a New Version of Gompertz Distribution
The Poisson Inverted Shifted Gompertz distribution is a new type of distribution that comes from the Poisson-generating family of distributions and is based on the "inverted shifted Gompertz distribution." This distribution has significant statistical characteristics, with clear formulations obtained mathematically. We use three distinct approaches to estimate the parameters of the distribution: maximum likelihood estimation (MLE), least-squares estimation (LSE), and Cramer-Von-Mises estimation (CVME). We undertake a simulation experiment to thoroughly assess the efficacy of maximum likelihood estimation (MLE). Empirical data from engineering and medical fields demonstrate the relevance of our suggested model. We meticulously evaluate the goodness-of-fit of the Poisson Inverted Shifted Gompertz distribution using several statistical tests and graphical techniques. Our suggested distribution demonstrates enhanced fitting capabilities and more flexibility compared to many widely used lifespan distributions. Furthermore, we investigate the Bayesian viewpoint of the proposed model by using Hamiltonian Monte Carlo (HMC) simulation methods. This detailed study gives you a full picture of how the Poisson Inverted Shifted Gompertz distribution can be used in many different areas.
Copyright (c) 2025 Laxmi Prasad Sapkota, Vijay Kumar, Getachew Tekle, Hleil Alrweili, Manahil SidAhmed Mustafa, M. Yusuf https://creativecommons.org/licenses/by/4.0
Analyzing Real Data by a New Heavy-Tailed Statistical Model
This study presents the power Mira distribution, an innovative three-parameter probability model that improves baseline distributions by including an extra shaping parameter. The suggested distribution has exceptional adaptability in representing various data characteristics, such as left and right skewness, declining trends, and unimodal patterns. These characteristics render it exceptionally appropriate for modeling risk-related data, an essential component of actuarial science and insurance analytics. We do an extensive theoretical study, delineating essential statistical features and offering a robust framework for parameter estimation. Critical risk metrics, including value-at-risk and tail value-at-risk, are calculated and assessed using comprehensive numerical simulations, validating the precision and efficacy of the suggested estimators. We illustrate the practical value of the power Mira distribution by applying it to a real-world insurance loss dataset and comparing its performance with established models. The findings underscore its exceptional goodness-of-fit and flexibility, affirming its capability as an effective instrument for risk assessment and financial modeling.
Copyright (c) 2025 Modern Journal of Statistics https://creativecommons.org/licenses/by/4.0