Iraqi Statisticians Journal (ISJ) is an open-access journal (without any fees) is published approximately semiannually by the Iraqi Association of Statistical Sciences. Its general objective is to promote and extend the use of statistical methods in all kinds of theoretical and applied disciplines. Iraqi Statisticians Journal (ISJ) is a global, scientific and open access journal. This journal has been published twice a year by the Iraqi Association of Statistical Sciences, Iraq. The Turnitin is used to prevent plagiarism and to ensure the originality of our submitted manuscripts. A double-blind peer-reviewing system is also used to assure the quality of the publication. The Iraqi Statisticians Journal was established in 2024 and publishes original research, review papers in the field of Statistical Science. ISJ is free of charge for publishing an accepted manuscript. The journal is financially supported by the Iraqi Association of Statistical Sciences. publishes original research papers and review papers. ISJ is dedicated to bringing together intellectual and professional scientists, as well as the public sectors who are engaged in efforts to understand the Statistical Science in the fields of: Statistics Mathematical Statistics Applied Statistics Stochastic Processes Regression Analysis Nonparametric Regression Generalized Linear Models Survival Analysis Spatial Statistics Multivariate Analysis Time Series and Forecasting Econometric Quality control High dimensional data
Iraqi Association of Statisticians Sciences
Licensed under a CC-BY license: https://creativecommons.org/licenses/by-nc-sa/4.0/
Forecasting public expenditures using ARDL–LSTM hybrid model
Public expenditure is regarded as the main tool for regulating fiscal policy and, consequently, affects the overall economic position of the country. This highlights the importance of high-quality forecasting, particularly when the objective is fiscal sustainability and the efficient allocation of resources. As economic behavior becomes more intricate and the relationships among variables increasingly intertwined, linear models are no longer sufficient for accurate prediction With the assumption that public expenditure is conditioned by public revenues, this work will endeavor to predict government expenditure through the application of a hybrid ARDL-LSTM model. The method combines Autoregressive Distributed Lag (ARDL) model to explain linear variations and fluctuations of the time series and a neural network model-Long Short-Term Memory (LSTM) to explain nonlinear trends. Based on the comparison criteria. The findings indicated that the hybrid ARDL-LSTM model is more effective in forecasting accuracy, based on the RMSE and MAPE criterion using both the estimation and testing samples, which confirms that the combination of linear and nonlinear model is more efficient in predicting economic time series.
ARDL, LSTM, ARDL-LSTM, Public Revenues, Public Expenditures.
Copyright (c) 2026 Sulaiman Hussien Jawad, Munaf Yousif Hmood (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
The Impact of Financial Sustainability and Structural Transformation on Investments Using QARDL Model Optimized by the Marine Predator Algorithm
The present article explores the asymmetric dynamic effects of fiscal sustainability and structural transformation on the private investment in Iraq over the timeframe (2008-2025) in a QARDL model optimized by Marine Predators Algorithm (MPA). The approach incorporates the use of MPA to improve on the efficiency of best lag choice followed by the estimation of the parameters to overcome non-convexity in the quantile loss function. The findings indicate asymmetric cointegration and a fiscal crowding out in both senses, and in both the structural transformation is revealed as the major source of driving in the low-credit period. The findings indicate that the emerging investments are very susceptible to inflation and parallel exchange rate shocks and therefore require specific monetary interventions. The paper suggests the use of the QARDL-MPA due to the high ability to predict nonlinear time series in economically uncertain settings.
Marine Predators Algorithm (MPA); QARDL Model; Investment Dynamics; Fiscal Sustainability; Structural Transformation; Iraqi Economy
Copyright (c) 2023 Mariam Jumaah Mousa , Munaf Yousif Hmood (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Activating the role of Artificial Intelligence for Optimised Resource Management in light of Meta-Goal Programming for Sustainable Agriculture
Optimising sustainable agriculture has become a vital objective for human survival, while economic progress has become the prime aim. The rapid population increase has to be faced by producing more from fewer resources. Thus, a comprehensive approach can be equipped to manage resources under-uncertainty conditions. This paper presents an integrated approach of Meta-Goal Programming with Artificial Intelligence (AI) to optimise resources in Malaysian sustainable agriculture. It has focused on rice and oil palm cultivation. Dual challenges have been addressed by this integrated approach, resource optimisation and environmental sustainability. A case study conducted to optimise resource-scarce agriculture has demonstrated significant improvements in water efficiency, crop yields, and ecological balance. This paper contributes a novel perspective to sustainable agriculture. Predictions have shown robust results which are aligned with actual data fields in terms of accuracy, 98% and 97% for rice and oil palm yield, respectively. The optimisation process has improved crop yields by reducing the usage of water and fertiliser use by 14% and 4% for rice and oil palm yield, respectively. The results validated the efficacy of the proposed approach, achieving the sustainable agriculture goals.
Copyright (c) 2026 Ibrahim Zeghaiton Chaloob (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
A Monte Carlo Simulation Study on the Performance of Linear and Quadratic Programming Estimators in Fuzzy ARDL Models
The the study analyzes the relative effectiveness of the Linear Programming (LP) and Quadratic Programming (QP) techniques to estimate the Fuzzy Autoregressive Distributed Lag (FARDL) model, which can be regarded as the generalization of the classical ARDL model and is used to estimate fuzzy dynamic relationships among variables. In this model parameters are represented as fuzzy numbers defined in terms of central value and spread, hence allowing the direct adoption of structural uncertainty as being a part of the model architecture instead of using a conventional stochastic error. A Monte Carlo simulation experiment was implemented to meet the objectives of the study with different sample size and the complexity of the lag structure with the objective of testing the performances of the two estimation methods in different data settings. The comparative evaluation was based on two performance measures: the Root Mean Square Error (RMSE) which is an indicator of the accuracy of the estimation of central parameters and the Fuzzy Degree (FD) which is an indicator that quantifies the amount of uncertainty in the estimates. The results of the simulations show that QP method is always better than the LP method in all the sample sizes and lag settings with lower values in RMSE and FD respectively in most cases. This advantage is very strong especially in small samples and it persists as the sample size increases.
Fuzzy ARDL, Linear Programming, Quadratic Programming, Monte Carlo Simulation, Estimation Performance
Beta Distributional Neural Networks for Bounded Outcome Prediction
This paper presents a new neural modeling system, named the Beta-Distributional Neural Network (BDNN), which is aimed at predicting restricted outcomes over the open unit interval (0,1). In contrast to the traditional neural networks, which produce deterministic point estimates, the proposed model provides direct predictions of the two shape parameters of the beta distribution ( and ), and thus, predictive mean and uncertainty can be estimated simultaneously. This is to achieve statistical coherence and computational stability, which is trained through maximum likelihood estimation by minimizing the negative log-likelihood. It is tested on BDNN using synthetic data sets, which have been built based on the data-generating curves, both linear and nonlinear, as well as a real-world colon cancer drug-response dataset. It makes comparative studies using ordinary least squares regression, classical beta regression and traditional feedforward neural network. Empirical findings prove that BDNN always has better predictive accuracy in terms of reduced RMSE and MAE values and has better probabilistic calibration based on negative log-likelihood. These results indicate the adequacy of incorporating distributional modelling with deep neural structures in the prediction of limited outcomes in medical and applied research areas.
Copyright (c) 2026 Ahmed Naziyah Alkhateeb (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Employing the Artificial Cuckoo Swarm Algorithm for Estimating Various Multiple Nonlinear Regression Models
Nonlinear regression models are widely used to model stochastic phenomena, and parameter estimation is essential for interpreting these models. Consequently, this research used the Artificial Cuckoo Swarm Algorithm to improve parameter estimation precision for three nonlinear models: Meyer 1, Meyer 5, and the Nelson Model. We employed two estimation techniques: nonlinear least squares (NLS) and the S estimation approach. To improve the efficacy of these two estimating approaches, they were integrated with the Artificial Cuckoo Swarm Algorithm. This work used simulation to evaluate the effectiveness of these two methodologies before and after the application of the algorithm, using sample sizes (50, 100, 150) and sigma levels (0.1, 0.5, 0.9). The mean squared error (MSE) is used as a benchmark for comparison. Simulation results demonstrate that the s-estimator method, particularly when combined with an AI algorithm, produces the smallest mean squared error (MSE) across all models. Furthermore, this technique achieved the lowest MSE values in almost every instance, even without the algorithm. In the pollution data for Iraq's Euphrates River, we employed the robust s-estimator method, along with the Cuckoo Swarm Algorithm, identified as optimal in simulation results, to estimate three nonlinear regression models with total dissolved solids as the dependent variable and sulfates and chlorides as the independent variables. The Cuckoo Swarm Algorithm method significantly improved the three nonlinear regression models included in the study, demonstrating its effectiveness. The findings indicated that chlorine and sulfates directly increase total dissolved solids in the Euphrates River.
Copyright (c) 2026 Ons Edin Musa, Sabah Manfi Redha (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Alpha Power Families of Distributions Article review
Generalizing probability distributions is a very important issue, as are many other practical issues statistics, All generalization methods have been performed by introducing additional parameters such as location, scale or shape. In the past few years, this branch of statistics has received considerable attention, and new classes of generalized distributions have been proposed. Here we provide a brief overview of this branch and also introduce several new families of distributions.
Copyright (c) 2026 Raya salim mohammed, Hayfa abdul jawad, Safwan N. Rashed, Heyam abd al-majeed (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Diagnose Insomnia by using Fuzzy Multiple Ordinal Logistic Regression
This research utilized a questionnaire designed to diagnose and analyze insomnia using the ordinal logistic regression model. The model was applied to traditional, fuzzy, and granular fuzzy data. Two hundred questionnaires were distributed across five locations, or "granules": the College of Nursing (40 questionnaires), the College of Administration and Economics (45 questionnaires), the College of Science (40 questionnaires), the College of Education (35 questionnaires), and the Middle Euphrates Department (35 questionnaires). The target audience included professors, staff, and male and female students from various age groups. The study concluded that the ordinal logistic regression model for a granular fuzzy sample was more accurate than using traditional and fuzzy data. Analysis of the phenomenon of insomnia revealed that it has physical and psychological effects, manifesting as fatigue, headaches, and poor concentration due to unhealthy habits such as excessive caffeine consumption, irregular sleep patterns, and excessive use of electronic devices
Insomnia Crisp set Fuzzy set Granular fuzzy set Ordinal logistic regression
Copyright (c) 2026 Bashar Khalid Ali, Sackineh Shamil Jasim (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
An improved unsupervised feature selection using fuzzy C-means clustering and Archimedes optimization algorithm
In this research, we propose a new choice of plant selection based on Archimedes Optimization Sales (BAS) in combination with a modified fuzzy c-mean algorithm. With marked patterns, BAS increases the unsecured learning of traditional unclear C-mines. Using these annotate patterns, BAS is able to model the geometry of each cluster correctly, emphasizing the properties that are most useful for discrimination against clusters. Patterns with high levels of cluster membership show small variance in the values ​​of these functions. These symptoms have strong discriminatory properties between clusters and other groups if there is a significant distance between the prototype of a cluster and the prototype of other clusters. We used BAS to classify patterns on many real benchmarks. Our learning method was the popular K-nest neighbor (FCM). Our results showed that the functional elections made by BAS increased generalization in all data sets.
. Binary Archimedes optimization algorithm
Copyright (c) 2026 Sarah Ghanim Mahmood Al- Kababchee, Ilham M Yacoob, Omar Saber Qasim3, Zakariya Yahya Algamal (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Enhancing the Iraqi Oil Revenue Forecasting: Comparative Evaluation of the ARIMA Model Extensions and Hybrid Models
The current study provides the necessary response to the problem of oil revenue prediction errors in Iraq because it explicitly analyzes the extensions of the autoregressive integrated moving average model (ARIMA) and the hybrid methodology. Although the results of the existing studies have already proven the efficacy of simple ARIMA structures, there remains the gaps in the understanding on how the more sophisticated alterations and hybrid approaches could further enhance predictive accuracy. We engage in a full comparative study of extensions of ARIMA models such as seasonal adjustment, integration of exogenous variables, and hybrid models that integrate machine learning and the traditional time series models. The suggested approaches are operated on monthly data on Iraqi oil revenues between 2021 and 2023 and tested with harsh methods of validation in form of calculation including AIC, BIC, MAE and MAPE. The findings indicate that the hybrid models are more successful than the single ARIMA models by reducing the MAPE by 15%. Moreover, residual diagnostics verify the stability of these hybrid methods where there is no severe autocorrelation and the properties of error distribution are improved. The research adds to the literature in that it provides empirical data on effectiveness of hybrid forecasting method in volatile commodity markets giving decision makers more valid instruments to use in financial planning. In addition, the results also underscore the need to have a combination of statistical and machine learning paradigm to identify complex non-linear trends on oil revenue data. Besides the contribution to the methodological discussion of time series forecasting, the given research also offers some practical insights.
Copyright (c) 2026 Mustafa Habib Mahdi (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Deep Functional Median Polish: A Robust Framework Integrating Functional Depth and Median-Based Decomposition for Long-Term Financial Time Series
This research builds upon the successive development of robust functional analysis methods, starting with the Median Polish (MP) algorithm, which provided a powerful additional model for handling bidirectional data, progressing through Functional Median Polish (FMP), and culminating in the integration of functional depth measures into a single framework. This work presents a new framework called Deep Functional Median Polish (Deep FMP), which combines the robustness of median statistics in the MP algorithm with the inherent geometric properties of functional depth measures to characterize the hierarchical structure of complex functional time series. Also applies the proposed model to financial data spanning 34 years, comprising 408 views structured in a 34×12 matrix. Each year is transformed into a smoothed function using Fourier's rule, and then PCA is used to derive a highly interpreted latent space, where the first component explains 94.3% of the total variance. Subsequently, the median model is applied to the latent space to separate the general, annual, seasonal, and residual components. The results demonstrated a high capacity for accurately reconstructing time-related behaviour, with near-normal residuals centred around 0.65, and a clear seasonal distribution that increases in January and December and decreases in the middle of the year. The results prove that combining depth measures with Median Polish provides high explanatory power and enhances the model's resistance to outliers, with clear applicability to economic data with complex time-related patterns. This model opens the way for future applications in forecasting, risk analysis, and detecting structural shifts in long-term functional data.
Copyright (c) 2026 Abdulsalam M. Sabri (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
The Odd Exponential–Rayleigh-Fréchet Distribution: Structural Properties, Estimation Methods, and Applications
This research presents a novel probability model called the Odd Exponential–Rayleigh–Fréchet (OERFR) distribution, which combines the power of the Odd-Exponentiated Rayleigh probability transformation with the flexibility of the Fréchet distribution, known for its ability to represent data with heavy tails and extreme values. The new model aims to address the problems that arise when using traditional distributions in the analysis of reliability and engineering data characterized by significant skewness and nonlinearity in risk behavior. The mathematical construction of the distribution is based on combining the T-X transformation with the odd-ratio transformation, adding two additional shape parameters to the basic distribution. These parameters enhance the distribution's ability to control tail shape, density slope, and the variety of risk function shapes. The basic functions of the model were derived. The study included conducting extensive simulation experiments using eight different estimation methods and at various sample sizes to evaluate the accuracy and statistical stability of each method. The results showed that some methods, such as QLS, MP, and WLSE, were superior in reducing bias and root-squared error at small and medium sample sizes. To confirm the applicability of the distribution, the model was tested on real data representing turbocharger failure times for diesel trucks. The OERFR model demonstrated a clear advantage over several competing distributions according to AIC, BIC, KS, AD, and CV metrics. This performance indicates that the new distribution possesses high flexibility and strong ability to represent real-world data in the areas of engineering, reliability, and extreme value analysis.
Copyright (c) 2026 Raghad W. Faris, Mundher A. khaleel (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Improved Estimator for Population Variance using two Auxiliary Information
This paper introduces a novel exponential estimator employing two auxiliary variables to estimate an unknown population variance. The estimator is designed to improve efficiency as compared with existing estimators. The bias and mean squared error (MSE) of the proposed estimator are obtained by a first-order Taylor series expansion. A theoretical comparison with several existing estimators is presented to demonstrate its superiority. To validate the theoretical results, an empirical study is conducted using three population datasets, complemented by a simulation study for cross-validation. The findings indicate that the proposed estimator consistently provides more precise estimates than the existing estimators. Additionally, we introduced a hybrid approach combining the exponential-type estimator with regression adjustment, further reducing bias and MSE under correlated auxiliary information.
Copyright (c) 2026 Sunil Kumar Yadav, Prof. Rajesh Singh (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Estimating the Order of Markov Chains Using Shannon Criterion and Akaike Criterion
Determining the order of a Markov chain is un important problem, as the correct decision to be made will be based on the specific order of that model. This research involves a Markov chain analysis of the gene sequence for the breast cancer-causing gene (BRCA1) and estimating its order using Shannon's Information Criterion and Akaike's Information Criteria. Selecting the appropriate order in modeling contributes to enhancing the understanding of the behavior of genes associated with breast cancer and enables early detection and the development of effective treatment strategies. The two aforementioned criteria were used, and the results showed that the order of this gene is the Second order using Shannon's criterion, and the Second -order model is the most accurate using Akaike's criteria.
Copyright (c) 2026 Alaa Abdallah Mahmoed (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
An Overview of Panel Data Analysis in Statistical and Econometric Research (Review)
Panel data combine features of both time series and cross-sectional data. Data on many economic or social units are observed in more than one time period. This framework enables the analysis of both within unit processes and between-unit heterogeneity, increases the efficiency of the estimations, and improves the fit of economic and statistical models. There are two essential types of panel data models: static panel models and dynamic panel models. Static models consider the dependent variable to be independent of its own past values, meaning that it does not contain any extrinsic dynamics. They are most commonly applied when there is no explicit time dependence to the phenomena of interest.
Copyright (c) 2026 Ban Ghanim Al-Ani (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
On the Analysis of Variance for Symmetrical Triangular and Normal Fuzzy Observations in a Randomized Complete Block Design
Fuzzy ANOVA has been successfully applied in one-way experimental designs, where fuzzy observations are modelled using symmetrical triangular fuzzy numbers (STFNs) and normal fuzzy numbers (NFNs). These approaches have proven helpful in various fields, such as environmental sciences, agriculture, and engineering, where data uncertainty is pervasive. However, previous work has focused mainly on Completely Randomized Designs (CRD), which assume homogeneity among experimental units. This assumption often oversimplifies real-world conditions where variability among experimental units cannot be ignored. Thus, this study proposed fuzzy Analysis of Variance (ANOVA) within a Randomised Complete Block Design (RCBD) framework using Symmetric Triangular Fuzzy Numbers (STFNs) and Normal Fuzzy Numbers (NFNs) to address measurement imprecision commonly encountered in experimental data. The methodology preserves the structural integrity of classical ANOVA while incorporating fuzziness to enhance data interpretation in the presence of uncertainty. Simulated datasets were analyzed to evaluate the performance of the proposed fuzzy ANOVA, and both treatment and block effects were found to be statistically significant, demonstrating the method’s effectiveness in detecting variability and treatment differences. STFNs provided a simple approach for modeling symmetric uncertainty, whereas NFNs offered smoother, more continuous representations, including visual tools such as triangular and Gaussian membership function plots, which further improved result interpretation and accessibility. The findings affirm that fuzzy ANOVA is a robust and interpretable extension of classical ANOVA, suitable for various areas where uncertain data is prevalent.
Copyright (c) 2026 Muhammed Mujitaba Muhammed, Yahaya Zakari, Sani Ibrahim Doguwa, Ibrahim Abubakar Sadiq, Naziru Isah Muhammed, Jamilu Garba (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
A Novel Wavelet-Based Approach for ANOVA in Longitudinal Data Analysis Using the First Derivative of the Laplace Function
Longitudinal data, characterized by repeated observations on the same subjects over time, present significant challenges for traditional statistical Analysis of Variance (ANOVA) methods, such as Repeated Measures ANOVA due to inherent intra-subject correlation and high dimensionality. This study introduced a novel wavelet-based ANOVA approach using the first derivative of the Laplace distribution to transform high-dimensional repeated measures data into a simplified Completely Randomized Design (CRD) structure, thereby facilitating classical ANOVA. The mathematical formulation and key properties (admissibility and energy localization) of this wavelet function are detailed. We rigorously proved that this wavelet satisfies the fundamental conditions required for signal analysis. Through a comprehensive simulation study, we demonstrated its effectiveness in preserving treatment differences, controlling Type I error rate, maintaining acceptable statistical power, and showing robustness to variations in the number of time points. The results validated the Laplace derivative wavelet as a powerful and reliable tool for dimensionality reduction and valid inference in longitudinal data analysis, offering a robust alternative to conventional repeated measures techniques.
Copyright (c) 2026 Naziru Isah Muhammad, Musa Tasi'u, Yakubu Aliyu, Umar Kabir Abdullahi (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
A New Generated Lifetime Model: Theory, Simulation and Application to Stress-Strength datasets
In this article, a new continuous model called the exponentiated Gompertz generated skew- t (EGGST) distribution based on the exponentiated Gompertz generalized distribution is introduced. The new model is capable of fitting skewed, long and heavy tailed dataset and is more flexible than the skew-t distribution which is considered a special case. Related theoretical properties of the new model such as the quantile function, ordinary moment, probability weighted moment, order statistics, Rényi and Shannon entropies were investigated. The model parameters were estimated using the maximum likelihood estimation and simulation study carried out to examine the finite sample performance of these estimates. The applicability of the new model was illustrated by means of well-known breaking stress and strength datasets.
Copyright (c) 2026 Obinna D. Adubisi (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Bathtub Curve in Reliability Analysis. A Review
The bathtub curve is a popular concept and an important tool in reliability analysis. It describes the pattern or shape of the hazard rate function of products or systems throughout their life cycles over time. It helps in understanding failure modes and identifying critical periods in the systems life cycle in many fields such as engineering, quality management, electronics manufacturing, and other applied fields. This paper reviews the stages of the curve in some detail, along with everything that has been written by researchers on statistical estimation methods for the failure rate at each stage, highlighting the distributions related to this curve. It also addresses how to identify the points of change and transformation in this curve and the extent of its impact on preventive maintenance. The paper concludes with some critical points and objections to the bathtub curve.
Copyright (c) 2025 Suhad Ahmed Abdullah , Rabab Abdulrida Saleh (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Running Mean Smoothing Technique of Extreme Exploratory Data Analysis with Application Using R Software
Exploratory Data Analysis (EDA) is a pivotal stage in statistical modeling and data analysis, comprising methods that support the identification of unknown patterns in data observations. Among the techniques employed, running mean smoothing, that sometimes known as the moving averages smoother, is openly applied to minimize the passing variations and highlight long-term trends. This paper clarifies the application of the running means smoothing method using the R software. The present way requires replacing each data observation with the average of its neighborhood within a known span, thereby detecting errors and outliers and enhancing the ability to interpret. The analysis shows how R opens the door to elastic and efficient achievement of smoothing for both contrived and real data. The outcomes proved that running mean as a technique of smoothing is effective in lighting invisible structures, detecting outliers, and providing insights into temporal dynamics, making it an important instrument in EDA.
Copyright (c) 2026 Qasim N. Husain (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
In this work, Lindley regression model is studied standing up Lindley distribution which is one of the generalized linear models. It is like with distributions for example Weibull, Exponential , Gamma and other distributions which are positive skew. This is Lindley Distribution. It aims to dealing with variables have positively skewed problems. The model has been composed and then reaching to to a required link function . Parameters are estimated by Maximum Likelihood Method by using Newton-Raphson because it is difficult to obtain closed parameters. In application , real data is used to compare a model depended on exponential distribution and other depended on Lindley`s distribution by using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) after showing by Kolmogorry - Smirnov Test that the dependent variable follows both distributions . The outcomes show that Lindley`s distributions provides accurate results comparing with results of the exponential distribution.
Copyright (c) 2023 Adnan Mostafa Al-Sinjary (Author); Hayder Sabah Tuama (Translator) https://creativecommons.org/licenses/by-nc-sa/4.0/
Construction of an Almost Unbiased Estimator for Population Variance Using Exponential - Sine Type Estimator
In this paper, we have proposed a generalized almost unbiased estimator for estimating the unknown finite population variance of the study variable , using auxiliary information under the exponential-cum-sine estimator framework. In many applications, the presence of bias in an estimator can be a significant drawback. Following the procedure of Singh and Singh (1991, 1993), we develop an estimator based on a single auxiliary variable, which is almost unbiased up to the order . Expressions for the bias and mean squared error (MSE) of the proposed estimator are derived up to the first order of approximation. To support the theoretical results, an empirical study using two real-life data sets has been conducted. Additionally, a simulation study confirms that the proposed estimator has lower bias (nearly zero) and achieves a minimum MSE equivalent to that of the regression estimator.
Copyright (c) 2025 Sunil Kumar Yadav, Rajesh Singh (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Threshold Effects Between Inflation and Economic MicGrowth From Nigeria
This study investigates the threshold effects between inflation and economic growth in Nigeria, covering the period under review. Using annual macroeconomic data, the paper employs descriptive statistics, unit root tests, the Autoregressive Distributed Lag (ARDL) bounds testing approach, and threshold regression analysis. The ARDL results indicate evidence of a long-run relationship between inflation and growth, while the Error Correction Model (ECM) confirms short-run adjustments. Threshold regression analysis identifies a critical inflation level beyond which inflation exerts a significantly negative impact on economic growth. Specifically, the estimated threshold is around 13 percent, consistent with prior findings in the literature. Below this level, inflation has a mild positive or insignificant effect, whereas above the threshold, its adverse effects dominate. The results highlight the importance of maintaining inflation within manageable bounds to sustain growth. Policy implications suggest that Nigerian monetary authorities should strengthen inflation targeting frameworks and coordinate fiscal policies to achieve macroeconomic stability. The findings contribute to the ongoing debate on the inflation-growth nexus and provide empirical evidence relevant for policy formulation in developing economies.
Copyright (c) 2025 Alhaji Umar Abubakar, Imam Akeyede (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
The Evolution of Estimation Methods and Applications of the Fama-MacBeth Model: A Review
This literary review offers a comprehensive analysis of the evolution of methods for estimating and using the Fama-MacBeth regression model in research. The paper traces the model's development from a simple tool for testing the Capital Asset Pricing Model (CAPM) to a complex statistical framework used to analyze multifactor models and complex phenomena. The review focuses on the key developments in the uses of the Fama-MacBeth model and its estimation. It also highlights the expansion of the model's applications. In conclusion, this review shows that the Fama-MacBeth model remains a vital and effective tool in financial research, and its methodological and applied evolution has made it more powerful and flexible in facing the challenges of analyzing complex financial data.
Copyright (c) 2025 Mariam Jumaah Mousa, Munaf Yousif Hmood (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Estimation of Transition Probabilities in Multi-State Survival Data
This study calculates nonparametric estimators including Kaplan-Meier, Nelson-Aalen and Aalen - Johnson for applying the Multi-State Model (MSM ) to analyze type IIIness-death transitions between alive and death followed by different duct cancer types (Breast, Lung , Brain , Ovary) through reduction techniques by using diminutions (k+1)*(k+1) for matrix , The package software program was used to generate elementary Nelson-Aalen and Kaplan-Meier estimator, reach a conclusion that the two procedure are producing result that are very close..
Copyright (c) 2025 Haider kareem Raheem , Hayder yahya mohammed (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
A proposal to Employ the Laplace Estimator and the IRWL Algorithm as Robust Methods in Segmented Linear Regression and Compare them with the Maximum Likelihood Estimator using Simulation
Segmented linear regression is one of the important statistical tools that is used to model and explain the behavior of some events in which changes gets suddenly or the behavior pattern of the event goes through transitional stages. The importance of this research lies in studying the proposal to employ the robust Laplace estimator within the method of estimating the parameters of the segmented linear regression model to give robustness to the estimation when there are outliers in the data. Then some updates were made to this method according to the iterative algorithm (IRWL) to get better robust estimates. On the practical side, the simulation experiment was conducted with several different sample sizes, and assuming several cases of pollution rates in the data (outliers) (15%, 10%, 5%, 0%), Then After implementing the simulation experiment and comparing the proposed methods with Muggeo's Maximum likelihood (ML) method using the (MSE) criterion, The experimental results showed the efficiency of the proposed methods when the data contains pollution ratios, and the iterative algorithm (IRWL) has proven its efficiency in obtaining the best estimate of the parameters compared to other methods. If there is no pollution in the data, the Muggeo's maximum likelihood (ML) method is the best for estimation.
Copyright (c) 2025 Mohammed Ahmed Abbas Al-Jubouri (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
A Generalized Shrinkage-type Estimator of Population Mean in Simple Random Sampling under conventional and non-conventional measures of auxiliary variables
In this study, a generalized shrinkage-type estimator of population mean in simple random sampling has been proposed. The proposed estimator is a combination of some of the known estimators in literature with the aim of obtaining estimators with higher efficiency. Its bias and mean squared error (MSE) have been derived using Taylor series up to the first order of approximation. The optimal MSE’s of the proposed class of estimators have been obtained. Theoretical comparison of the proposed shrinkage-type estimator has been also made with other existing related ratio estimators of the population mean using auxiliary information. The conditions under which the proposed shrinkage-type estimators perform better than the other existing estimators of population mean are given. Validation of results from both simulation and real data sets application reveals that the proposed shrinkage-type estimators performed better than some existing related ratio estimators considered in this work as they are having lower mean squared errors and higher percent relative efficiencies (PREs).
Copyright (c) 2025 Emmanuel J. Ekpenyong, Loveline Chiamaka Okoro, Theophilus Obijuru Nelson (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Evaluation of Relative Loss in Odd Generalised Exponential Burr Type X and Truncated Odd Generalised Exponential Burr Type X Distributions
This paper presents derivation entropy measures for two types of distributions: the Odd Generalised Exponential Burr type X distribution (OGEBX) and the truncated Odd Generalised Exponential Burr type X distribution (TOGEBX). The relative loss was achieved by testing a set of different parameter values. In the context of certain distributions, the optimistic results of this study can be applied. Based on the lowest value of each distribution, a numerical comparison was made between the entropy measures to select the optimal one. The relative loss was then determined using all six measures. When the OGE Burr Type X distribution is not used on [0, ∞], but the truncated OGE Burr Type X distribution on [0, t] is used.
Copyright (c) 2025 Murtadha M.Jasim, Moudher Kh. Abdal-hammed, Mizal Alobaidy, Alaa A. Khalaf (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Evaluating the Performance of Bayesian Estimates for Burr XII Inverse Rayleigh Parameters Using MCMC
This work applied multiple Bayesian approaches to estimate the parameters of the Burr XII Inverse Rayleigh (BXII-IR) Distribution. For Bayesian estimators, needed priors distribution for the parameters and certain loss functions such squared error, general entropy, and linear-exponential, owing to the unavailability of closed-form solutions for Bayesian estimates with these loss functions. Bayesian estimate employing the Markov Chain Monte Carlo (MCMC) approach were assessed for performance. The simulation results for Bayesian methods indicate that all methods consistently estimate the parameters, with the LN2 loss function estimator demonstrating the highest efficiency as assessed by mean squared error (MSE), root mean squared error (RMSE), bias, Highest Posterior Density Intervals (HPD), average interval length (AIL), and coverage probability (CP).
Copyright (c) 2025 Alaa A. Khalaf, Mundher A. Khaleel, Danial Mazarei, Ahlam H. Tolba, Akeem A. Adepoju (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/
Enhancing the Cosine-Lomax Distribution: A New Exponentiated Version with Improved Flexibility and Real-World Applications
In this paper, we introduce a novel flexible probability distribution called the Exponentiated Cosine Lomax distribution (ECLD), developed by compounding the exponentiated family with the cosine Lomax distribution. The proposed model incorporates an additional shape parameter, enhancing its flexibility to model complex real-world data with heavy tails, skewness, and non-monotonic hazard rates. We derive key statistical properties of the ECLD, including moments, moment-generating function, quantile function, and hazard rate. The model parameters are estimated using the maximum likelihood estimation (MLE) and maximum product of spacings (MPS) methods. A comprehensive simulation study is conducted to assess the consistency and efficiency of the estimators. To demonstrate the practical applicability of the ECLD, we analyze two real-world datasets. Comparative studies with existing models, including the Odd Frechet Lomax, half logistic Lomax, cosine Lomax, Lomax and sine Lomax distributions, reveal that the proposed ECLD provides a significantly better fit based on goodness-of-fit criteria such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Kolmogorov-Smirnov (K-S) test. The findings suggest that the ECL distribution is a robust alternative for modeling skewed and heavy-tailed data in various fields.
Copyright (c) 2025 Ibrahim Ali, Alhaji Modu Isa, Sule Omeiza Bashiru, Ibrahim Ismaila Itopa (Author) https://creativecommons.org/licenses/by-nc-sa/4.0/