Iraqi Statisticians Journal

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.

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.

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.

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

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.

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.