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.
In this paper, we derived an estimators and parameters of Reliability and Hazard function of new mix distribution ( Rayleigh- Logarithmic) with two parameters and increasing failure rate using Bayes Method with Square Error Loss function and Jeffery and conditional probability random variable of observation. The main objective of this study is to find the efficiency of the derived of Bayesian estimator compared to the to the Maximum Likelihood of this function using Simulation technique by Monte Carlo method under different Rayleigh- Logarithmic parameter and sample sizes. The consequences have shown that Bayes estimator has been more efficient than the maximum likelihood estimator in all sample sizes with application
In this paper, we derived an estimator of reliability function for Laplace distribution with two parameters using Bayes method with square error loss function, Jeffery’s formula and conditional probability random variable of observation. The main objective of this study is to find the efficiency of the derived Bayesian estimator compared to the maximum likelihood of this function and moment method using simulation technique by Monte Carlo method under different Laplace distribution parameters and sample sizes. The consequences have shown that Bayes estimator has been more efficient than the maximum likelihood estimator and moment estimator in all samples sizes
A non-parametric kernel method with Bootstrap technology was used to estimate the confidence intervals of the system failure function of the log-normal distribution trace data. These are the times of failure of the machines of the spinning department of the weaving company in Wasit Governorate. Estimating the failure function in a parametric way represented by the method of the maximum likelihood estimator (MLE). The comparison between the parametric and non-parametric methods was done by using the average of Squares Error (MES) criterion. It has been noted the efficiency of the nonparametric methods based on Bootstrap compared to the parametric method. It was also noted that the curve estimation is more realistic and appropriate for the re
... Show MoreThis paper concerns with deriving and estimating the reliability of the multicomponent system in stress-strength model R(s,k), when the stress and strength are identical independent distribution (iid), follows two parameters Exponentiated Pareto Distribution(EPD) with the unknown shape and known scale parameters. Shrinkage estimation method including Maximum likelihood estimator (MLE), has been considered. Comparisons among the proposed estimators were made depending on simulation based on mean squared error (MSE) criteria.
Due to the wide distribution through the Iranian Plateau, especially in its western parts adjacent to Iraq’s northeastern borders, the occurrence of Brandt’s Hedgehog
Sn effect on the phase transformation behavior, microstructure, and micro hardness of equiatomic Ni-Ti shape memory alloy was studied. NiTi and NiTiSn alloys were produced using vacuum induction melting process with alloys composition (50% at. Ni, 50% at.Ti) and (Ni 48% at., Ti 50% at., Sn 2% at.). The characteristics of both alloys were investigated by utilizing Differential Scanning Calorimetry, X- ray Diffraction Analysis, Scanning Electron Microscope, optical microscope and vicker's micro hardness test. The results showed that adding Sn element leads to decrease the phase transformation temperatures evidently. Both alloy samples contain NiTi matrix phase and Ti2Ni secondary phase, but the Ti2Ni phase content dec
... Show MoreMany people take protein supplements in an effort to gain muscle. However, there is some controversy as to whether this is really effective. There is evidence suggesting that consuming high level s of protein may in fact have negative side effects for health. The current study included 29 young Iraqi building muscles in two different groups (taken and not protein supplements) (age range=17-31 years), the cases were selected from family, friends, college students, and Gyms), from November 2014 to March 2015. A careful history was obtained from each volunteer including age, duration of sports, type of supplements, and family history of diseases. Some biochemical parameters like (glucose, urea, uric acid, creatinine, bilirubin, serum protei
... Show MoreReceipt date:12/7/2020 accepted date:24/1/2021 Publication date:31/12/2021
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The constant characteristic of international relations is the constant change due to political, economic and military developments in addition to technology, and this in turn has led to many transformations in the concept of power, its uses, and the elements that form power and its distribution, and according to those variables, the concept of power has shifted from hard to soft, up to smart powe
... Show MoreIn this paper, estimation of system reliability of the multi-components in stress-strength model R(s,k) is considered, when the stress and strength are independent random variables and follows the Exponentiated Weibull Distribution (EWD) with known first shape parameter θ and, the second shape parameter α is unknown using different estimation methods. Comparisons among the proposed estimators through Monte Carlo simulation technique were made depend on mean squared error (MSE) criteria
A restrictive relative clause (RRC hereafter), which is also known as a defining relative clause, gives essential information about a noun that comes before it: without this clause the sentence wouldn’t make much sense. A RRC can be introduced by that, which, whose, who, or whom. Givon (1993, 1995), Fox (1987), Fox and Thompson (1990) state that a RCC is used for two main functions: grounding and description. When a RRC serves the function of linking the current referent to the preceding utterance in the discourse, it does a grounding function; and when the information coded in a RRC is associated with the prior proposition frame, the RRC does a proposition-linking grounding function. Furthermore, when a RRC is not used to ground a new di
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