The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the Power Function Distribution (PFD-I) to estimate it. The conjugate prior function of the shape parameter θ was considered as a combination of two different prior distributions such as gamma distribution with Erlang distribution and Erlang distribution with exponential distribution and Erlang distribution with non-informative distribution and exponential distribution with the non-informative distribution. We derived Bayes estimators for shape parameter θ of the Power Function Distribution (PFD-I) according to different loss functions such as the squared error loss function (SELF), the weighted error loss function (WSELF) and modified linear exponential (MLINEX) loss function (MLF), with two different double priors. In addition to the classical estimation (maximum likelihood estimation). We used simulation to get the results of this study, for different cases of the shape parameter of the Power Function Distribution used to generate data for different samples sizes.
Background: White-spot lesion is one of the problems associated with the fixed orthodontic treatment. The aims of this in-vitro study were to investigate enamel damage depth on adhesive removal when the adhesive were surrounded by sound, demineralized or demineralized enamel that had been re-mineralized prior to adhesive removal using 10% Nano-Hydroxy apatite and to determine the effect of three different adhesive removal techniques. Materials and methods: Composite resin adhesive (3M Unitek) was bonded to 60 human upper premolars teeth which were randomly divided in to three groups each containing ten sound teeth and ten teeth with demineralized and re-mineralized lesions adjacent to the adhesive. A window of 2 mm was prepared on the bucca
... Show MoreThe art of postmodernism has undergone a number of changes in the course of art and art schools, as art has left the traditional means and paved the way for this artistic transformation to change the materials, techniques, methods and visions as a result of the changes that occurred in the thought and this change played an important role in the artist's vision, To demolish and destroy all of the above and to reconsider the formal systems and intellectual contexts and expressive modes, so it is necessary for the whole art to keep up with the variables of the era and its elements. The current research aims to: "Detect the transformations of form in postmodern art in the projects of students of the Department of Art Education".
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... Show MoreThe basic idea of the Main Outfall Drain, MOD, was to construct a main channel to collect saline drained water of the irrigation projects within central and southern parts of Iraq and discharge it down to the Arabian Gulf. The MOD has a navigation lock structures near Addalmage Lake at station 299.4km. This structure is designed to ensure navigation within the MOD. The water level difference upstream the cross regulator and the downstream conjugation structure is about 9m. This head difference can be used to generate electrical power by constricting a low head power plant. This study aimed to utilize the head difference in navigation lock structures for power generation. Different operation condition an
... 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 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 MoreIn this work, the nuclear electromagnetic moments for the ground and low-lying excited states for sd shell nuclei have been calculated, resulting in a revised database with 56 magnetic dipole moments and 41 electric quadrupole moments. The shell model calculations are performed for each sd isotope chain, considering the sensitivity of changing the sd two-body effective interactions USDA, USDE, CWH and HBMUSD in the calculation of the one-body transition density matrix elements. The calculations incorporate the single-particle wave functions of the Skyrme interaction to generate a one-body potential in Hartree–Fock theory to calculate the single-particle matrix elements. For most sd shell nuclei, the experimental data are well rep
... Show MoreThis paper represents an experimentalattempt to predict the influence of CO2-MAG welding variables on the shape factors of the weld joint geometry. Theinput variables were welding arc voltage, wire feeding speed and gas flow rate to investigate their effects on the shape factorsof the weld joint geometry in terms of weld joint dimensions (bead width, reinforcement height, and penetration). Design of experiment with response surface methodology technique was employed to buildmathematical models for shape factors in terms of the input welding variables. Thepredicted models were found quadratic type and statistically checked by ANOVA analysis for adequacy purpose. Also, numerical and graphical optimizations were carried out
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