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.
The objective of this research is to study experimentally and theoretically the girder vertical load share of the curved I-Girder bridges subjected to the point load in addition to the self-weigh and supper imposed dead loads. The experimental program consist of manufacturing and testing the five simply supported bridge models was scaled down by (1/10) from a prototype of 30m central span. The models carriageway central radii are 30 m, 15m or 10m. The girder spacing of the first two models is 175 mm with an overall carriageway width of 650mm. The girder spacing of the other three bridge models is 200mm with the overall carriageway width of 700 mm. The overall depth of the composite section was 164 mm. To investigate the effect of live load
... Show MoreIn this research work an attempt has been made to investigate about the Robustness of the Bayesian Information criterion to estimate the order of the autoregressive process when the error of this model, Submits to a specific distributions and different cases of the time series on various size of samples by using the simulation, This criterion has been studied by depending on ten distributions, they are (Normal, log-Normal, continues uniform, Gamma , Exponential, Gamble, Cauchy, Poisson, Binomial, Discrete uniform) distributions, and then it has been reached to many collection and recommendations related to this object , when the series residual variable is subject to each ( Poisson , Binomial , Exponential , Dis
... Show MoreThe current research aims to analyze the mathematics book for the first intermediate grade according to the dimensions of mathematical power by answering the following question: What is the percentage of the availability of the dimensions of mathematical power included in the content of the mathematics textbook for first-grade students, average, in its first, and second parts for the academic year 2020-2021, approved by the Iraqi Ministry of Education / General Directorate of Curricula? The research community was determined by middle school mathematics books, and middle school students for middle ,and high school day schools affiliated to the Directorate of Education in Dhi Qar, and by the intentional test, the research sample was s
... Show MoreThe aim of this work is study the partical distribution function g(r12,r1) for Carbon ion cases (C+2,C+3,C+4) in the position space using Hartree-Fock's Wave function, and the partitioning technique for each shell which is represented by Carbon Ions [C+2 (1s22s2)], [C+3 (1s22s)] and [C+4 (1s2)]. A comparision has been made among the three Carbon ions for each shell. A computer programs (MATHCAD ver. 2001i) has been used texcute the results.
In this paper, we have extracted Silica from rice husk ash (RHA) by sodium hydroxide to produce sodium silicate. 3-(chloropropyl)triethoxysilane (CPTES) functionalized with sodium silicate via a sol-gel method in one pot synthesis to prepare RHACCl. Chloro group in compound RHACCl replacement in iodo group to prepere RHACI. The FT-IR clearly showed absorption band of C-I at 580 cm-1. Functionalized silica RHACI has high surface area (410 m2/g) and average pore diameter (3.8 nm) within mesoporous range. X-ray diffraction pattern showed that functionalized silica RHACI has amorphous phase .Thermogravemitric analysis (TGA) showed two decomposition stages and SEM morphology of RHACI showed that the particles have irregu
... Show MoreConditional logistic regression is often used to study the relationship between event outcomes and specific prognostic factors in order to application of logistic regression and utilizing its predictive capabilities into environmental studies. This research seeks to demonstrate a novel approach of implementing conditional logistic regression in environmental research through inference methods predicated on longitudinal data. Thus, statistical analysis of longitudinal data requires methods that can properly take into account the interdependence within-subjects for the response measurements. If this correlation ignored then inferences such as statistical tests and confidence intervals can be invalid largely.
In this research is estimated the function of reliability dynamic of multi state systems and their compounds and for three types of systems (serial, parallel, 2-out-of-3) and about two states (Failure and repair) depending on calculating the structur function allow to describing the behavior of
In this research, we find the Bayesian formulas and the estimation of Bayesian expectation for product system of Atlas Company. The units of the system have been examined by helping the technical staff at the company and by providing a real data the company which manufacturer the system. This real data include the failed units for each drawn sample, which represents the total number of the manufacturer units by the company system. We calculate the range for each estimator by using the Maximum Likelihood estimator. We obtain that the expectation-Bayesian estimation is better than the Bayesian estimator of the different partially samples which were drawn from the product system after it checked by the
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