In this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of Bayes estimators of the shape parameter of the Maxwell distribution decreases with the increase of Jeffreys prior constants. The results also show that values of Bayes estimators are almost close to the maximum likelihood estimator when the Jeffreys prior constants are small, yet they are identical in some certain cases. Comparison with respect to loss functions show that Bayes estimators under the modified squared error loss function has greater MSE than the squared error loss function especially with the increase of r.
The process of evaluating data (age and the gender structure) is one of the important factors that help any country to draw plans and programs for the future. Discussed the errors in population data for the census of Iraqi population of 1997. targeted correct and revised to serve the purposes of planning. which will be smoothing the population databy using nonparametric regression estimator (Nadaraya-Watson estimator) This estimator depends on bandwidth (h) which can be calculate it by two ways of using Bayesian method, the first when observations distribution is Lognormal Kernel and the second is when observations distribution is Normal Kernel
... Show MoreIn this paper, we find the two solutions of two dimensional stochastic Fredholm integral equations contain two gamma processes differ by the parameters in two cases and equal in the third are solved by the Adomain decomposition method. As a result of the solutions probability density functions and their variances at the time t are derived by depending upon the maximum variances of each probability density function with respect to the three cases. The auto covariance and the power spectral density functions are also derived. To indicate which of the three cases is the best, the auto correlation coefficients are calculated.
In this study, we made a comparison between LASSO & SCAD methods, which are two special methods for dealing with models in partial quantile regression. (Nadaraya & Watson Kernel) was used to estimate the non-parametric part ;in addition, the rule of thumb method was used to estimate the smoothing bandwidth (h). Penalty methods proved to be efficient in estimating the regression coefficients, but the SCAD method according to the mean squared error criterion (MSE) was the best after estimating the missing data using the mean imputation method
Fusidic acid (FA) is a well-known pharmaceutical antibiotic used to treat dermal infections. This experiment aimed for developing a standardized HPLC protocol to determine the accurate concentration of fusidic acid in both non-ionic and cationic nano-emulsion based gels. For this purpose, a simple, precise, accurate approach was developed. A column with reversed-phase C18 (250 mm x 4.6 mm ID x 5 m) was utilized for the separation process. The main constituents of the HPLC mobile phase were composed of water: acetonitrile (1: 4); adjusted at pH 3.3. The flow rate was 1.0 mL/minute. The optimized wavelength was selected at 235 nm. This approach achieved strong linearity for alcoholic solutions of FA when loaded at a serial concentrati
... Show MoreLinear motor offers several features in many applications that require linear motion. Nevertheless, the presence of cogging force can deteriorate the thrust of a permanent magnet linear motor. Using several methodologies, a design of synchronous single sided linear iron-core motor was proposed. According to exact formulas with surface-mounted magnets and concentrated winding specification, which are relying on geometrical parameters. Two-dimensional performance analysis of the designed model and its multi-objective optimization were accomplished as a method to reduce the motor cogging force using MAXWELL ANSYS. The optimum model design results showed that the maximum force ripple was approximatrly reduced by 81.24%compared to the origina
... Show MoreThis research aims at building a proposed training program according to the self-regulated strategies for the mathematics teachers and to identify the effect of this program on relational Mathematics of teachers. The sample of the research was (60) Math teachers; (30) teachers as experimental group and (30) teachers as control group. The results of the current research reacheded that the proposed training program according to some self-managed learning strategies, meets the needs of trainees with remarkable effectiveness to improve the level of their teaching performance to achieve the desired goals. Training teacher according to self-managed learning strategies is effective in bringing about the transition of training to their students
... Show MoreIn this research, some robust non-parametric methods were used to estimate the semi-parametric regression model, and then these methods were compared using the MSE comparison criterion, different sample sizes, levels of variance, pollution rates, and three different models were used. These methods are S-LLS S-Estimation -local smoothing, (M-LLS)M- Estimation -local smoothing, (S-NW) S-Estimation-NadaryaWatson Smoothing, and (M-NW) M-Estimation-Nadarya-Watson Smoothing.
The results in the first model proved that the (S-LLS) method was the best in the case of large sample sizes, and small sample sizes showed that the
... Show MoreIn the analysis of multiple linear regression, the problem of multicollinearity and auto-correlation drew the attention of many researchers, and given the appearance of these two problems together and their bad effect on the estimation, some of the researchers found new methods to address these two problems together at the same time. In this research a comparison for the performance of the Principal Components Two Parameter estimator (PCTP) and The (r-k) class estimator and the r-(k,d) class estimator by conducting a simulation study and through the results and under the mean square error (MSE) criterion to find the best way to address the two problems together. The results showed that the r-(k,d) class estimator is the best esti
... Show MoreIn order to obtain a mixed model with high significance and accurate alertness, it is necessary to search for the method that performs the task of selecting the most important variables to be included in the model, especially when the data under study suffers from the problem of multicollinearity as well as the problem of high dimensions. The research aims to compare some methods of choosing the explanatory variables and the estimation of the parameters of the regression model, which are Bayesian Ridge Regression (unbiased) and the adaptive Lasso regression model, using simulation. MSE was used to compare the methods.