Gumbel distribution was dealt with great care by researchers and statisticians. There are traditional methods to estimate two parameters of Gumbel distribution known as Maximum Likelihood, the Method of Moments and recently the method of re-sampling called (Jackknife). However, these methods suffer from some mathematical difficulties in solving them analytically. Accordingly, there are other non-traditional methods, like the principle of the nearest neighbors, used in computer science especially, artificial intelligence algorithms, including the genetic algorithm, the artificial neural network algorithm, and others that may to be classified as meta-heuristic methods. Moreover, this principle of nearest neighbors has useful statistical features. The objective of this paper is thus to propose a new algorithm where it allows getting the estimation of the parameters of Gumbel probability distribution directly. Furthermore, it overcomes the mathematical difficulties in this matter without need to the derivative of the likelihood function. Taking simulation approach under consideration as empirical experiments where a hybrid method performs optimization of these three traditional methods. In this regard, comparisons have been done between the new proposed method and each pair of the traditional methods mentioned above by efficiency criterion Root of Mean Squared Error (RMSE). As a result, (36) experiments of different combinations of initial values of two parameters (λ: shift parameter and θ: scale parameter) in three values that take four different sample sizes for each experiment. To conclude, the proposed algorithm showed its superiority in all simulation combinations associated with all sample sizes for the two parameters (λ and θ). In addition, the method of Moments was the best in estimating the shift parameter (λ) and the method of Maximum Likelihood was in estimating the scale parameter (θ).
Pareto distribution is used in many economic, financial and social applications. This distribution is used for the study of income and wealth and the study of settlement in cities and villages and the study of the sizes of oil wells as well as in the field of communication through the speed of downloading files from the Internet according to their sizes. This distribution is used in mechanical engineering as one of the distributions of models of failure, stress and durability. Given the practical importance of this distribution on the one hand, and the scarcity of sources and statistical research that deal with it, this research touched on some statistical characteristics such as derivation of its mathematical function , probability density
... Show MoreThe purpose of this paper is to model and forecast the white oil during the period (2012-2019) using volatility GARCH-class. After showing that squared returns of white oil have a significant long memory in the volatility, the return series based on fractional GARCH models are estimated and forecasted for the mean and volatility by quasi maximum likelihood QML as a traditional method. While the competition includes machine learning approaches using Support Vector Regression (SVR). Results showed that the best appropriate model among many other models to forecast the volatility, depending on the lowest value of Akaike information criterion and Schwartz information criterion, also the parameters must be significant. In addition, the residuals
... Show MoreThe research took the spatial autoregressive model: SAR and spatial error model: SEM in an attempt to provide practical evidence that proves the importance of spatial analysis, with a particular focus on the importance of using regression models spatial and that includes all of the spatial dependence, which we can test its presence or not by using Moran test. While ignoring this dependency may lead to the loss of important information about the phenomenon under research is reflected in the end on the strength of the statistical estimation power, as these models are the link between the usual regression models with time-series models. The spatial analysis had been applied to Iraq Household Socio-Economic Survey: IHS
... Show MoreA simple analytical method was used in the present work for the simultaneous quantification of Ciprofloxacin and Isoniazid in pharmaceutical preparations. UV-Visible spectrophotometry has been applied to quantify these compounds in pure and mixture solutions using the first-order derivative method. The method depends on the first derivative spectrophotometry using zero-cross, peak to baseline, peak to peak and peak area measurements. Good linearity was shown in the concentration range of 2 to 24 μg∙mL-1 for Ciprofloxacin and 2 to 22 μg∙mL-1 for Isoniazid in the mixture, and the correlation coefficients were 0.9990 and 0.9989 respectively using peak area mode. The limits of detection (LOD) and limits of quantification (LOQ) wer
... Show MoreTheresearch took the spatial autoregressive model: SAR and spatial error model: SEM in an attempt to provide a practical evident that proves the importance of spatial analysis, with a particular focus on the importance of using regression models spatial andthat includes all of them spatial dependence, which we can test its presence or not by using Moran test. While ignoring this dependency may lead to the loss of important information about the phenomenon under research is reflected in the end on the strength of the statistical estimation power, as these models are the link between the usual regression models with time-series models. Spatial analysis had
... Show MoreDespite the importance of sustainable development and its dimensions in developing performance and supporting competitive advantage in economic units, there is a gap and lack of coordination between Combined Assurance providers (management, internal audit, external audit) to report on sustainable development, and the research aims to propose a model for the Combined Assurance report to achieve development sustainable development in the Iraqi economic units, especially the Baghdad Municipality, enables assurance providers to coordinate efforts that lead to the achievement of Combined Assurance, The research found the proposed model for the Combined Assurance report in achieving sustainable development in the Iraqi economic units, es
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We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed (LSD)
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