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.
Compaction curves are widely used in civil engineering especially for road constructions, embankments, etc. Obtaining the precise amount of Optimum Moisture Content (OMC) that gives the Maximum Dry Unit weight gdmax. is very important, where the desired soil strength can be achieved in addition to economic aspects.
In this paper, three peak functions were used to obtain the OMC and gdmax. through curve fitting for the values obtained from Standard Proctor Test. Another surface fitting was also used to model the Ohio’s compaction curves that represent the very large variation of compacted soil types.
The results showed very good correlation between the values obtained from some publ
... Show MoreThe Light and the Dark is the fourth novel in a series written by Charles Percy Snow where it tackles a phase of gifted scholar and remarkable individual Roy Calvert as he search for a source of power and meaning in life to relieve his inner turmoil. The character Roy Calvert is based on Snow's friend, Charles Allbery who exposes the message the character of Roy intends to convey in a certain phase of his life and the prophecy the novel carries amid catastrophe so widespread in the thirties of the twentieth century
In this paper, a new seven-parameter Mittag-Leffler function of a single com-plex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.
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 MoreDue 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
Stumpff functions are an infinite series that depends on the value of z. This value results from multiplying the reciprocal semi-major axis with a universal anomaly. The purpose from those functions is to calculate the variation of the universal parameter (variable) using Kepler's equation for different orbits. In this paper, each range for the reciprocal of the semi-major axis, universal anomaly, and z is calculated in order to study the behavior of Stumpff functions C(z) and S(z). The results showed that when z grew, Stumpff functions for hyperbola, parabola, and elliptical orbits were also growing. They intersected and had a tendency towards zero for both hyperbola and parabola orbits, but for elliptical orbits, Stumpff functions
... Show MoreThe research is aimed at dynamics the dynamics of the artistic form within the theater and the dynamics of this movement in the development of the form and the multiplicity of meaning. This research came to address a problem of great importance in the creation of the image and the form of theatrical presentation. The evolution and transformation within the display system requires a dynamic structure that enables the form of growth and growth. The aim of the research was to identify the dynamics of form in the Iraqi theater. The researcher then identified two terms: form and motor.
In the theoretical framework, it was divided into two sections: the first (the dynamics of the artistic form) and the second (the dynamics of the act of dir
Many 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 MoreA 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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