Iraqi Statisticians Journal

1

Inferential Methods for the Dagum Regression Model

Pages: 1-8 English

Abstract

The Dagum Regression Model, introduced to address limitations in traditional econometric models, provides enhanced flexibility for analyzing data characterized by heavy tails and asymmetry, which is common in income and wealth distributions. This paper develops and applies the Dagum model, demonstrating its advantages over other distributions such as the Log-Normal and Gamma distributions. The model's parameters are estimated using Maximum Likelihood Estimation (MLE) and the Method of Moments (MoM). A simulation study evaluates both methods' performance across various sample sizes, showing that MoM tends to offer more robust and precise estimates, particularly in small samples. These findings provide valuable insights into the analysis of income inequality and wealth distribution using the Dagum model.

2

Application of Neural Networks for Predicting the Exchange Rate of the Iraqi Dinar Against the US Dollar and Comparison with the Box-Jenkins Method for Time Series 2015-2022

Pages: 9-28

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Abstract

Recently, there have been changes in the exchange rate of the Iraqi dinar against foreign currencies, which are considered important financial indicators that affect the labor market and the currency exchange market. In order to monitor the changes in the exchange rate of the Iraqi dinar against the US dollar and to anticipate future stages and the direction of the exchange rate changes, the aim of the research is to predict the exchange rate of the Iraqi dinar against the US dollar for the coming years by applying the Box-Jenkins methodology and neural networks. This is done to compare the traditional predictive models, such as ARIMA, with the neural network model, which demonstrated its prediction accuracy by reducing the Mean Squared Error (MSE) through training the network, selecting the appropriate model, and choosing the best architecture to represent the time series.

The study included a time series representing the exchange rates of the Iraqi dinar against the US dollar from January to December for the years 2015-2022. The data was sourced from the 2021/2022 annual statistical group issued by the Central Statistical Organization of Iraq, with data from the Central Bank of Iraq. For the analysis of the time series, the GRETL statistical program was used, and the Matlab R 2019b program was utilized for forecasting when using neural networks.

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Estimation Methods: Inference Classical and Bayesian of Extended Inverse Exponential Distribution

Pages: 29-42 English

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Abstract

The parameters of the Burr XII-Inverse Exponential (BXII-IE) distribution were estimated in this work using a variety of Bayesian and non-Bayesian (Inference Classical) approaches. Methods like Maximum likelihood, least squares, weighted least squares, Maximum product space estimators, and Anderson Darling were developed for non-Bayesian estimators. Due to the lack of closed-form solutions for Bayesian estimates for certain loss functions squared error, general entropy, and linear-exponential and prior distributions for the parameters, Bayesian estimators had to be implemented. Bayesian estimation utilizing the Markov Chain Monte Carlo (MCMC) approach and seven non-Bayesian estimate techniques were tested for performance.

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Statistical Evaluation of the Gompertz-Fréchet distribution: Statistical Elasticity Analysis Using Simulation, Estimation and Application

Pages: 43-56 English

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Abstract

This paper deals with the analysis of the Gompertz-Fréchet (GoFr) distribution, which combines the Gompertz family and the Fréchet distribution, where the statistical properties of proposed distribution are studied and accurate estimation methods for the distribution parameters are developed. Monte Carlo simulation was employed to evaluate the performance of three estimation methods: the Maximal likelihood method (MLE), the least squares method (LSE), and weighted least squares method (WLSE). The simulation included different sample sizes ranging from n=50 to 200, and the results were analyzed using criteria such as bias, mean square error (MSE), and root mean square error (RMSE). The results showed that the MLE method is the most accurate and efficient, as the bias and MSE decreased with the increase in sample size. The GoFr distribution was also applied to real data and compared with six other distributions using statistical accuracy criteria such as AIC and BIC. The results confirmed that the GoFr distribution is superior in its fit to the data compared to other models, which reflects its flexibility and effectiveness in analyzing data of complex nature

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On the Theory and Pliability of Regressogram Decomposition: Application and Simulation Sensitivity of the Olanrewaju-Olanrewaju Kernel-Based Regressogram

Pages: 57-73 English

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Abstract

This paper studies the pliability of regressogram decomposition as a technique of modeling bivariate random measurements of (X_1,Y_1),…,(X_n,Y_n) either via equal-width bins or via linear smoother with the use of nonparametric, Olanrewaju-Olanrewaju, and machine-learning Boxcar kernels. The mentioned kernels were separately incorporated into the Nadaraya-Watson kernel-estimator as a generalized Mercer kernel. The optimal bandwidth needed as a smoothing parameter for impelling the kernel-based regressogram was derived using Generalized Cross-Validation (GCV). Furthermore, finite and countable sample size bound required for the regressogram modeling was ascertained for reasonable sample sizes needed for effective optimization of coefficients, deductive measurable of some error indexes and strongly universally consistent estimator. In conclusion, the Olanrewaju-Olanrewaju kernel-based regressogram was notably sensitive with miniature scale estimated (σ^2) and GCV estimates in application to real life dataset and simulation study to the nonparametric Doppler regression function.

6

Extension of the Weibull Survival Regression Based on Sine Type II Topp-Leone-G Family of Distribution: Properties and Application

Pages: 74-90 English

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7

Performance analysis of classical and fuzzy series components system of reliability estimation of New X-Lindley distribution simulation with comparative

Pages: 105-123 English

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8

Stability Analysis of Threshold Autoregressive Distributed Lag (TARDL(1,1,1)) Models Using Dynamical Approach: Applied Study of Limit Cycle Condition and Orbital Oscillations

Pages: 91-104 English

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Abstract

This research aims to study the stability condition of the Threshold Autoregressive Distributed Lag [TARDL(1,1,1)] model using dynamic Approach. The limit cycle condition was applied to the model, where the stability of the model was analysed through differential equations that reflect oscillations and cycles, firstly will prove and present the limit cycle condition for this model. Two examples were presented: the first one satisfies the stability of limit cycle and stabilizes at a constant value, while the second one does at satisfy the condition and continuous to oscillate. MATLAB programing was used to plot the model trajectories and explain whether it is stable or not. The results showed that the model stabilizes when the condition is satisfied, while not satisfying it leads to continuous oscillations. Finally a practical application was conducted on real data to determine the stability or not of the models at the limit cycle.

9

Hypothesis Testing for Non-Normal Multiple Compact Regression Model

Pages: 124-137 English

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Abstract

Generalized multivariate transmuted Bessel distribution belongs to the family of probability distributions with a symmetric heavy tail. It is considered a mixed continuous probability distribution. It is the result of mixing the multivariate Gaussian mixture distribution with the generalized inverse normal distribution. On this basis, the paper will study a multiple compact regression model when the random error follows a generalized multivariate transmuted Bessel distribution.
Assuming that the shape parameters are known, the parameters of the multiple compact regression model will be estimated using the maximum likelihood method and Bayesian approach depending on non-informative prior information. In addition, the Bayes factor was used as a criterion to test the hypotheses. A Gaussian distribution rule selects the bandwidth parameter and the kernel function based on the Gauss kernel function and quartic kernel function. It estimates the model parameters are under quadratic loss function. The researchers concluded that the posterior probability distribution of ▁θ is a multivariate t distribution. Applying the findings to real data related to the jaundice percentage in the blood component as a response variable, red blood cell volume and red blood cell sedimentation as parametric influencing variables, and white and red cells as nonparametric influencing variables, the researchers concluded that when the shape parameters increase, the values of the mean square error criteria of ▁θ And the variance parameter decreases.

10

Reliability Evaluation of a Hybrid Renewable Energy Complex System with Weibull Failure Laws Using Minimal-Cut Set Approach

Pages: 138-145 English

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Abstract

Many rural areas in Nigeria are still grappling with epileptic power supply while others are awaiting access to the national grid due to their remote locations. To meet the essential energy demands at these areas, penetration of renewable energy sources has become a policy priority for the society and nation at large. Renewable energy sources are a viable alternative solution due to their abundant available nature, clean energy source, environmentally friendly, and emission -free. Due to their intermittent available property, hybrid renewable energy sources are used to mitigate this drawback. In this study, hybrid renewable complex energy system with five components subsystem is evaluated. The complex system was first converted to a series-parallel system using the Minimal-cut set approach. The variables associated with repair and failure rates of each component is assumed to follow a Weibull probability density function. The derivation of Mean Time to System Failure (MTSF) and reliability of the system was obtained via reliability mathematics techniques. The MTSF and reliability of the complex renewable system were calculated for random values of component parameters such as failure rate (λ), shape parameter (β) and operating time (t) of the system components. The dynamic responses of these reliability indices have been presented graphically and numerically with arbitrary numerical values of the component’s parameters. The results reveal that reliability declines as failure rate, shape parameter, and operating time rise. The MTSF was also found to decrease with an increase in both failure rate and shape parameter of each system components. This study, therefore, shows that the system reliability can be increased by operating it at a minimal value of failure rate and shape parameter respectively.

11

Data Modelling and Analysis Using Odd Lomax Generalized Exponential Distribution: an Empirical Study and Simulation

Pages: 146-162 English

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Abstract

This study is based on the formulation of a new probabilistic model called the
generalized singular Lomax exponential distribution using the singular Lomax
generator and the exponential distribution. The proposed distribution is very flexible in
modelling age data with both decreasing and increasing (non-monotonic) shapes. We
define the probability density function (pdf) and cumulative distribution function
(CDF) for the proposed distribution. Some mathematical properties of the proposed
distribution such as the quantum function and moments are derived and for the
incomplete moments the Renyi entropy of the proposed distribution is also obtained.
Furthermore, the paper discusses model parameters in three different techniques, with
Monte Carlo simulations to determine the efficiency of estimating the HOLGE
distribution, with a comparison with three benchmarks to determine the best
estimation method. A practical application is also carried out on two types of data that
include the survival times of 72 guinea pigs infected with virulent tuberculosis bacilli,
where the efficiency of the HOLGE distribution analysis is determined by comparing
it to six other distributions using 4 information criteria and 4 statistical measures,
which demonstrated the efficiency and flexibility of the HOLGE distribution

12

Estimating the Fuzzy Regression Panel Data Model Based on Approximate Bayesian Computation with Application

Pages: 163-176 English

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Abstract

This study aims to estimate the parameters of fuzzy regression for panel data using a fixed regression model. To achieve greater accuracy in estimation, an approach is proposed that combines two estimation methods, leveraging the advantages of both probabilistic and traditional methods. The fixed regression model provides an integrated framework for analyzing cross-sectional and temporal data, contributing to a comprehensive analysis of panel data. This approach was applied to water pollution data of the Euphrates River using the fuzzy fixed regression model. The root mean square error (RMSE) criterion was used to compare different estimation methods. The results showed that the proposed methods generally outperformed the estimation methods, and gave better performance than probabilistic and traditional estimation methods. This study presents a new application for panel data using fuzzy regression, highlighting the benefit of combining traditional and probabilistic methods to achieve better estimations.

13

New Stochastic Restricted Estimator: A Step Towards Improved Modeling in Linear Regression

Pages: 177-187 English

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Abstract

Here, we propose a new convex linear combination estimator, called the New Mixed Estimator (NME), for multiple linear regression models with stochastic linear constraints on unknown parameters and multicollinearity between explanatory variables. The Ordinary Mixed Estimator (OME) and the Biased Stochastic Restricted Liu-type Estimator (SRLIT), two well-known estimators, are integrated to create the NME. Using Mean Square Error (MSE) as the main performance parameter, we examine the statistical characteristics of the NME and theoretically compare it to both OME and SRLIT to show its superiority. According to our research, the NME routinely performs better than the OME and SRLIT in terms of overall efficacy and statistical characteristics. Additionally, we provide a numerical example to clearly support these findings.

14

Estimation of Transition Probabilities in Multi-State Survival Data

Pages: 188-194 English

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15

Modified Weibull-Fréchet Distribution Properties with Application

Pages: 195-216 English

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Abstract

In this paper, develop new statistical distribution From within the continuous distributions based on the Hybrid Weibull-G family and the Frechet distribution, called the Hybrid Weibull Frechet. This development comes by adding two new parameters to the basic distributions in order to give more flexibility and suitability to the basic Frechet distribution for reading and modeling real-world data. Also present the basic functions of the new distribution (pdf, CDF). In addition, the paper will present an expansion of these functions and an expansion of the powers on which a number of statistical properties of the two proposed distributions will be built, such as the moments function, Incomplete Moments, Probability Weighted Moments, the survival function, the quantity function, and four types of entropy and disparity measures that represent a small number of... Numerous mathematical and statistical features of the developed distribution. A parameters were also estimated using the MLE. In order to obtain a distribution characterized by high flexibility to match different types of real data, a simulation was conducted to demonstrate the efficiency of estimating the unknown parameters of the new distribution using the maximum likelihood method. In addition, each distribution was tested on two types of real data of different sizes. The proposed new distribution proved highly flexible for the data when compared to other distributions through the use of some statistical standards such as AIC, BIC, CAIC, and HQIC. The results obtained showed the extent of flexibility and accuracy that supports what was discussed in the theoretical aspect.

16

Properties of New Extension of Exponentiated Exponential Distribution with Application

Pages: 217-229 English

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Abstract

Lifetime data modeling is vital topic that has received extensive attention in the modern statistical literature. This study aims to present a new distribution resulting from the expansion of the Exponentiated Exponential distribution using the [0,1] Truncated Nadarajah – Haghighi – G family, and this distribution is named [0,1]TNHEE several mathematical properties of the new distribution are studied, including density function, cumulative distribution, survival function, hazard function, moments, moment generated function, entropies (Shannon Rényi, and Delta), Lorenz and Bonforoni function, residual function, in addition to rank statistic and maximum likelihood estimators. The distribution was applied to real world data representing the survival times of 72 guinea pigs infected with tuberculosis. The results showed that the new distribution outperformed several competing distribution, including [0,10TEEEE, BeEE, KuEE, EGEE, and WeEE using statistical comparison criteria such as AIC, BIC, CAIC, and HQIC, as well as the Kolmogorov – Smirnov test, which yielded a high p-value (0.603), confirming the goodness of fit. The results showed that the new distribution has high flexibility and excellent interpretability for real-world data, making it a effective candidate for medical and engineering applications.

17

A New Type I Half Logistic Topp-Leone Kumaraswamy Distribution: Properties and Applications to Covid 19 data

Pages: 230-245 English

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