IRAOI JOURNAL OF STATISTICAL SCIENCES

In this paper, the survival function of the Weibull distribution was estimated by the Classical Maximum Likelihood Estimate Method for the scale and shape parameters, and then the efficiency of the estimated parameters was calculated based on the mean square error and compared with the proposed method that deals with the contamination problem before estimating the parameters of the survival function for Weibull distribution through the use of Wavelets (Daubechies2), (Symlet3), and (Coiflit4) with several different methods of estimating the level of thresholding depending on the rule of soft. For the purpose of estimating and comparing the efficiency of the proposed method with the classical method, simulations were carried out for several different cases of the values for scale and shape parameters of Weibull distribution, contamination percentages, and different sample sizes as well as real data based on a MATLAB code designed for this purpose, the statistical program (SPSS) and the (Easy Fit) program. The study showed the efficiency of the precision parameters estimate for Weibull distribution when there was a data contamination problem when using the proposed method compared to the classical method.

The purpose of this study is to determine whether an enhanced confound model representing bivariate wavelet-autoregressive integrated moving average with exogenous variable BWARIMAX is beneficial for predicting monthly traffic accidents. A wavelet-based multiresolution analysis MRA, conducted before the ARIMAX model fitting, shows that the performance of ARIMAX models in predicting traffic accidents can be significantly improved. The method described in this study identifies the ideal wavelet function, wavelet transform, and number of decomposition levels for the MRA and consequently considerably improves forecast accuracy. The analysis of the study demonstrated the superiority of the suggested approach and revealed that utilizing the BWARIMAX method, we can extract more information from the series, which enhances the performance of the original ARIMAX model in terms of predicting. Additionally, it has been demonstrated through extensive empirical testing using a wide range of wavelet families that Daubechies and Coiflet wavelets are excellent choices for denoising data. Furthermore, the study concluded that out of the two wavelet families, the performance of the Coiflet wavelet of order 3 was better.

Hidden Markov models were developed to analyze bioinformatics data that have attracted the attention of researchers because of their critical importance in the life of living organisms. The aim of this paper was to determine the quality of the nitrogenous base substituted for the MT-ND5 gene chain of humans and mice. The proposed algorithm using the Viterbi algorithm in the Hidden Markov model proved to be good in determining the quality of the nitrogenous base substituted for the MT-ND5 gene chain of humans and mice, depending on the high match ratios obtained and the low sum of squared errors. A computer program was designed for this purpose and the algorithm was programmed in MATLAB R2017b language, and from the practical application of the algorithm it is seen that the Hidden Markov model is a particularly powerful approach to determine the match ratio up to a high classification accuracy.

Road traffic and deaths accidents are the most complex and dangerous system of all road systems that people deal with on a daily basis. In addition to the loss of life, there is also a lot of material damage to the society. Therefore, we aim to study this effective topic through the Box-Jenkins model and the Elman Neural Network which are very appropriate to choose the best and most appropriate model for the number of accidents and the number of deaths from traffic accidents in the Iraqi Kurdistan Region according to monthly during the years (2014-2021).
Finally, we compared the results between both models. It was concluded that the results of the Elman model (1:2,5) are better than the SARIMA (1,1,1)(0,1,1)12 model for the number of traffic accidents, and the results of the Elman(1:2,3) model are better than the SARIMA (0,1,1)(1,1,2)12 model for the number of deaths from traffic accidents based on statistical measures (RMSE, MAE, MAPE), which we used it for comparison. Statistical analysis is performed using the software (Statgraphics V.19) and the program (Matlab V.18a)

In this paper, our main objective is to use a latent variable model and to propose a suitable model with features such as a nonlinear fixed covariates and latent variables based on different models that could be described both based on mathematical as well as structural model. We also used dichotomous (Binary) variables in Non-Linear latent variables model for two populations by using Bayesian approach as well as the Gibbs sampling method to find the comparison, differences and similarities based on different data points and estimate them accordingly. We have also included Hidden continuous normal distribution that can be both censored and truncated based on the type and need of the moment using which we can screen the different aspects involved in analysing the data and further Gibbs sampling method can also be used in the same filtering. It is often used in a view to solve the problem related to dichotomous data and accordingly relate it to different variables as a continuous normal distribution. We can also make use of various inferences derived based on the statistical results that include all the perspectives considering the scope of standard errors, most common methods, simplified approaches, and highest posterior density problem for testing and so on. All the theories are substantiated using real data and the results obtained from them using the OpenBugs program. It’s obvious from the results of DIS that the results of interval censored normal distribution was the best, then, the results of interval truncated normal distribution and, finally, the results of continuous normal distribution.

The focus of this paper is to approximate the cumulative distribution function (CDF) of the t distribution, which represents a combined distribution of the normal distribution and gamma distribution. The study utilizes the approximate formula proposed by Polya for the normal distribution, originally introduced in 1945. By applying this final formula to various points and comparing the results with the tabulated values of the t distribution, the researchers found that the absolute error between the two sets of values is negligible. It should be noted that this error slightly increases with higher degrees of freedom. Furthermore, the study observed that the absolute errors remain consistent when multiple points are selected at the same degrees of freedom. These findings have practical implications for statistical analysis, as they offer a time and effort-saving approach for obtaining CDF values associated with the t-distribution.

The UN's International Organization for Migration (IOM) reported that Iraq is the fifth-most affected country by soaring temperatures. This requires assessing the risks associated by accurately understanding the behaviour of these extreme events. A deep investigation of the behaviour of 2m air temperature has been done, by spatially modeling this event using extreme value copula with Pickands dependence. The investigation of the 2m extreme air temperature in Iraq concluded that the symmetric extreme-value copula models are suitable to consider in the modeling. Nine extreme value copula models were constructed from one parameter family copulas (Hüsler-Reiss, Gumbel, and Galambos), and two parameters model t-EV, after adopting the spatial context. Fifty locations were randomly sampled from 1517 locations divided into two parts, 40 for modeling, and 10 for validation. The Composite Maximum Pseudo-Likelihood estimation method has been used in the modeling. According to the AIC information criterion, we selected 4 models as candidates (Hüsler-Reiss A and B; Gumbel, and Galambos). Due to the slight difference in the criterion values among the four candidate models, the Kullback-Leibler (KL) divergence method between the non-parametric and parametric pairwise extreme-value copulas has been evaluated by the validation dataset, to choose the best-fitted model. The Hüsler-Reiss A was the best-fitted model, due to the high KL density around zero of all the pairwise in the validation dataset.

Abstract :The process of selecting statistical variables that contain information related to the effect on the dependent variable has a fundamental role in accurate statistical modeling. In time series and when there are a large number of an autoregressive (AR) variables in the model, selecting the most effective AR variables among a large set of autoregressive variables (high dimensional) with prior time lags is important for more accurate results. The elastic net method is one of the methods used for selecting the best model and conducting a joint estimation of the linear models, which contributes to the selection of the actually influencing variables and ignoring others among a very large set (high dimensional) of autoregressive variables. In this study, the elastic network method will be used to select and estimate the autoregressive parameters in the time series model. Caenorhabditis elegans (CE) will use time series data for the movement of Caenorhabditis elegans, represented by tangent angles of the wave motion. The univariate time-series model of CE movement was selected via the elastic network method and the hybrid (Elastic-AR) autoregressive model after multi-processes of selecting autoregressive variables. According to the results, the selected parameters in the AR model matched the Elastic-AR hybrid model, with clear superiority in the results of the hybrid method and with high accuracy. Therefore, it is possible to conclude the possibility of using the proposed hybrid method to obtain the best model for the high-dimensional time series dataset with the least number and the most influential of variables, which reduces effort and costs and increases the accuracy of these models.
Keywords: selecting autoregressive variables, time series high dimensional, autoregressive model AR, Elastic-Net, Elastic-AR hybrid model.

Numerous research projects in many area concentrate on phenomena that develop over extended times rather than those that are only visible at particular discrete intervals in time. The mechanisms underlying these observations are frequently selected to be represented by time-homogeneous stochastic processes (Markov model). To evaluate the suitability of these models, we process two test statistics. The first test evaluates the overall quality of fit, and the second test evaluates regional departures from homogeneity in the temporal direction. Information on the spread of two Kidney diseases is examined prior to death for 40 kidney disease patients in Rizgari Hospital during the period (2020-2022) . The results of both tests were significant. The statistical social science state SPSS has been used for this study.

inverse Gaussian regression model is one of the important models, which is widely used in many applications. The inverse Gaussian model is placed in tables of families of generalized linear models as it is one of the basic models. Like other regression models, the model may contain many independent variables, which negatively affects the accuracy of the model and its simplicity in interpreting the results. This study aims to use the modified crow search algorithm and compare it with other methods in selecting the variables in the inverse Gaussian regression model using simulation and real data. The results showed that the proposed method contributes to reducing the average square error of the model and achieves better performance compared to other previously used methods.

In this study, it has been aimed to introduce a new statistical distribution called Exponential Power - Chen by using the method suggested by Alzaatreh et al. (2013). Some statistical properties such as moments, coefficies of skewness and kurtosis, random number generator for Exponential Power Chen (EP-CH) distribution are obtained. Moreover, the maximum likelihood estimators (MLEs) for unknown parameters of EP-CH distribution have been derived and a Monte Carlo simulation study based on mean square errors and biases of this estimators for various sample sizes have been performed. Finally, an application using real data set has been presented for this new distribution.

The accuracy of forecasting the time series of relative humidity in its maximum and minimum cases is important for controlling environmental impacts, damages and risks. In this study, the support vector regression (SVR) method and the random forest (RF) method will be used, depending on the principle of auto regressive (AR) and the autocorrelation (AC), which is the main characteristic of time series in general. The Lags of original time series will be depended as the explanatory (input) variables while the original series will be as target variable. This structure is fitted with the AC principle because the current observation will be depending on time lags in each time step of time series variable. Comparisons of the forecasting results will be performed by using SVR , RF methods and compared to the classical method of analysing time series which is the integrated autoregressive and moving average (ARIMA) model. The SVR and RF methods were employed due to their importance in improving the forecast results, as they are the ideal solution to the problem of non-linearity of the data, as well as the problem of heterogeneity in the climate data, especially as a result of the fact that they contain many seasonal and periodic compounds, which may lead to inaccurate forecast. The forecast of the time series of relative humidity in its minimum and maximum cases was studied in this study for one of the agricultural meteorological stations in the city of Mosul-Iraq. The results of this study reflected the superiority of both SVR method and RF method compared to the classical method represented by the ARIMA model. The results also included the superiority of the RF method in forecasting the training period compared to the SVR method, which was more balanced despite that, as it superiority the results of ARIMA in forecasting the training period and the testing period, while it was its forecast performance is slightly better than the forecast results of the RF method in the test period.

This paper focused on estimating the survival time of real data for breast cancer patients in Nineveh province for the period between 2007- 2013. Robust estimation formulas were proposed and dealt with the Cox regression model in survival analysis. Determine the degree of hazard faced by women infected with this disease. Where it was proposed to use some Robust weights, and some classical variance estimators were replaced with Robust estimators to get an efficient estimation of the model, and also the suggestion of Robust weight functions. The Huber weight function was the best and was applied with the three templates to get the best model for the person of the variables that influence the occurrence of the event.

Time series data are widely used in many fields including microbiology data. It is necessary to know how to classify the category to which observation belongs by using statistical classification methods and machine learning and deep learning algorithms. The study of the movement of some types of nematodes as one of the types of microorganisms including Caenorhabditis elegans (CE) is important to determine the actions and their impact on the life of the worms. In this study the CE motion time series data were represented by its wave motion angles which would be the study case. the non-linearity and uncertainty will be among the most common problems in this type of data that may lead to classifications that are not accurate. Convolutional Neural Network (CNN) will be used as one of the deep learning techniques and it is a non-linear method used to classify CE movement as a dependent variable in binary cases based on images of wave motion angles as an independent variable and its use will lead to accurate results because it is a suitable non-linear method to deal with Study data to solve nonlinearity and uncertainty problems through digital data visualization. Logistic regression (LR) and kernel method were also used to classify CE angles of movement. The AR(p) rank was used to determine the structure of the used methods. And by comparing the results between the methods used, it was found that the CNN method is superior to the other methods used. Therefore, it is possible to conclude that the use of the CNN method, which is based on pictorial classification, leads to accurate classification results compared to other methods based on numerical classification.

This study aims to build a prediction model for the influential variables of evaporation in the Kurdistan region - Iraq, using the concept of regression and cluster analysis. The methods common guide the work to highlight the strengths of each technique, and the possibility of using hierarchical cluster analysis (nearest neighbor, furthest neighbor, and median) to improve the predictive accuracy of regression models. The variables affecting the evaporation rate were classified using weather data from meteorological stations in the Kurdistan Region, Iraq for the period from January 2020 to December 2022, and The adjusted R2, MSE, and RMSE values were used as indicators of the efficiency of the model’s performance.
The study found that clustering before regression analysis leads to improve prediction accuracy by classifying and identifying homogeneous independent variables within one cluster that are different from the rest of the clusters.

in this paper, real data was collected on people infected with the Covid-19 epidemic in the city of Mosul for the period from 1/11/2020 to 1/4/2021. Where the items of the patient\'s form (resident/output) were approved in the city\'s hospitals, which contain a current reality of the pathological condition, in addition to the historical situation of the injured person in terms of health. This data was analyzed and build an SQL-Server database system to store patient’s data that was collected for analysis through Microsoft Excel. The main objective of the paper is to diagnose the main factors that control the issue of the spread of the Covid-19 epidemic by building a model that simulates all the social components of the city of Mosul in terms of the standard of living, cultural, class decline, and the rest of the factors that describe Mosul society, and then the data collected from health centers are reflected on that model. Through the study and analysis of the data, it was found that the relationships between the incidence of the epidemic and the factors that were identified in the data collection

Clinical studies indicate a close relationship between some diseases and the presence of specific interactions between genetic factors. As is the case in many studies, revealing genetic interactions that have a significant impact on the emergence of genetic diseases requires extensive statistical analyses. Because of the enormous volume of genetic data in the human race, it was necessary to develop statistical methods adapted to deal with high-dimensional data. Multifactor Dimensionality Reduction (MDR) is one of the leading nonparametric algorithms in this field. The algorithm reduces the dimensions of genetic data to obtain the most important interaction that has a direct impact on increasing the likelihood of genetic diseases appearing. In its composition, the algorithm relies on a set of nonparametric procedures to diagnose genetic interference with the highest impact exclusively on binary response variables. Like any statistical method, this algorithm is not devoid of weaknesses and application limitations, so the algorithm had to be developed to overcome the obstacles. One of the weaknesses of this algorithm is that the algorithm cannot handle data sets with ordinal response variable. Some researchers have developed a generalization of the multifactor dimensionality reduction algorithm to enable it to work with ordinal data. However, the generalized algorithm is more complex than the original algorithm. Therefore, we proposed developing the original algorithm in a simple way by employing ordinal logistic regression to classify individuals in the sample, while keeping all steps of the original algorithm unchanged. On the other hand, the MDR algorithm adopts a non-parametric method to verify the significance of the interferences nominated in the algorithm. This nonparametric procedure is based on the idea of permutational tests, and it consumes a very long time compared to parametric procedures that relies on theoretical approaches. Some researchers have suggested using the generalized extreme value distribution to verify the statistical significance of candidate interactions, but this method has only been used with continuous and binary dependent variables. In this research, the theoretical method based on the generalized extreme value distribution was employed instead of the permutational tests adopted in the algorithm when the response variable is of the ordinal type.

This paper deals with finding a formula for the stress-strength reliability function P(T Simulation study is used to determine the best estimator; the results showed that Bayesian estimation using informative priors based on Weighted Square Error Loss Function is the best estimator For the equal sizes , and Bayesian estimation using Non-informative priors based on Weighted Square Error Loss Function is the best estimator when the size of the stress sample (Z) larger than the size of (X,T) , and Maximum Likelihood Estimator is the best estimator For the rest sizes.

In this study, it has been aimed to introduce a new family called as Exponential Power - X family of distributions by using the method suggested by Alzaatreh et al. (2013). Exponential Power Weibull (EP-W) distribution as a special sub model of this new family is discussed and its some statistical properties has been obtained. Moreover, the maximum likelihood estimators (MLEs) for unknown parameters of EP-W distribution have been derived and a simulation study based on MSEs and bias of this estimator for various sample sizes has been performed. Finally, an application with real data set has been presented.
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The research presented a comparative study in time series analysis and forecasting using VAR models, which depend on the existence of a significant relationship between the studied variables, and ARIMAX models, which depend on the linear effect of the independent variables (model input) on the dependent variable (model output). The models were analyzed using time series data for the Iraqi general budget for the period (2004-2020), which represents foreign reserves and government spending. Time series of government expenditure was forecast for the years (2021-2024) and a comparison was made between the efficiency of the models estimated through the mean square error (MSE) criterion. The analysis was carried out using the MATLAB program, and the results of the analysis concluded that the VAR model was more efficient than the ARIMAX model for this data and the increase in foreign reserves and government spending for the Iraqi will continue during the coming period (2021-2024).