This Book is the second edition that intended to be textbook studied for undergraduate/ postgraduate course in mathematical statistics. In order to achieve the goals of the book, it is divided into the following chapters. Chapter One introduces events and probability review. Chapter Two devotes to random variables in their two types: discrete and continuous with definitions of probability mass function, probability density function and cumulative distribution function as well. Chapter Three discusses mathematical expectation with its special types such as: moments, moment generating function and other related topics. Chapter Four deals with some special discrete distributions: (Discrete Uniform, Bernoulli, Binomial, Poisson, Geometric, Negative Binomial and Hypergeometric) with their mathematical formulas of p.m.f., C.D.F. and m.g.f. Chapter Five deals with some special continuous distributions: (Uniform, Normal, Exponential, Gamma and Beta) with their mathematical formulas of p.m.f., C.D.F. and m.g.f. Many solved examples are intended in this book (obtaining mean and variance of distributions by m.g.f.). Chapter Six introduces univariate discrete and continuous transformations, i.e., one dimensional variables and their yielding probability distributions. Chapter Seven devotes to truncation of distributions from left, right or both sides, beside the probability distribution of order statistics. Chapter Eight discusses mathematical features of joint, marginal and conditional distributions, as well as independency via covariance and correlation of bivariate distributions. Chapter Nine deals with some special topics such as getting distribution for some transformation from multidimensional random variables by using moment generating function (m.g.f.) and cumulative distribution function (C.D.F.) Many solved examples (about 100) are intended in this book, in addition to a variety of unsolved relied problems (about 150) at the end of each chapter to enrich the statistical knowledge of our readers.
The theory of probabilistic programming may be conceived in several different ways. As a method of programming it analyses the implications of probabilistic variations in the parameter space of linear or nonlinear programming model. The generating mechanism of such probabilistic variations in the economic models may be due to incomplete information about changes in demand, production and technology, specification errors about the econometric relations presumed for different economic agents, uncertainty of various sorts and the consequences of imperfect aggregation or disaggregating of economic variables. In this Research we discuss the probabilistic programming problem when the coefficient bi is random variable
... Show MoreIn this paper, we investigate the connection between the hierarchical models and the power prior distribution in quantile regression (QReg). Under specific quantile, we develop an expression for the power parameter ( ) to calibrate the power prior distribution for quantile regression to a corresponding hierarchical model. In addition, we estimate the relation between the and the quantile level via hierarchical model. Our proposed methodology is illustrated with real data example.
Friction Stir Welding (FSW) is one of the most effective solid states joining process and has numerous potential applications in many industries. A FSW numerical tool, based on ANSYS F.E software, has been developed. The amount of the heat gone to the tool dictates the life of the tool and the capability of the tool to produce a good processed zone. Hence, understanding the heat transfer aspect of the friction stir welding is extremely important for improving the process. Many research works were carried out to simulate the friction stir welding using various softwares to determine the temperature distribution for a given set of welding conditions. The objective of this research is to develop a finite element sim
... Show MoreThe accretion circumstellar disk of young stars and the Brown dwarf plays an essential role in the formation and evaluation of the planet. Our main work in this paper is to investigate the geometrical shape model for the protoplanetary disk around one of the Brown Dwarfs. The photometric measurements for the brown dwarf CFHT-BD-Tau 4 were extracted from the Vizier archive. We used a numerical simulation to build a model of the spectral energy distribution of our target CFHT-BD-Tau 4. The spectral energy distribution model was fitted with observational data for the brown dwarf CFHT-BD-Tau 4. A transitional disk has been assumed around CFHT-BD-Tau 4. We obtained physical properties of the two disks and the size of the gap between them
... Show MoreThe approach of the research is to simulate residual chlorine decay through potable water distribution networks of Gukookcity. EPANET software was used for estimating and predicting chlorine concentration at different water network points . Data requiredas program inputs (pipe properties) were taken from the Baghdad Municipality, factors that affect residual chlorine concentrationincluding (pH ,Temperature, pressure ,flow rate) were measured .Twenty five samples were tested from November 2016 to July 2017.The residual chlorine values varied between ( 0.2-2mg/L) , and pH values varied between (7.6 -8.2) and the pressure was very weak inthis region. Statistical analyses were used to evaluated errors. The calculated concentrations by the calib
... Show MoreA groundwater quality assessment has been carried out in northeast part of Anbar governorate in western Iraq. We analyzed hydrochemical parameters such as pH, electrical conductivity, total dissolved solids presence of ions to describe groundwater quality. The study area has the only confined aquifer within the geological formation extended in area. Values of groundwater hydrochemical parameters were ranged from (7) to (7.9) for ph, (1599) to (6800) µmhos/cm for electrical conductivity (EC) and (1048) to (4446) mg/l for total dissolved solids (TDS). The origins and types of groundwater in the area were of marine origin and MgCl2 water type while only (6) samples were of continental origin and Na2SO4 wate
... Show MoreIn this research we solved numerically Boltzmann transport equation in order to calculate the transport parameters, such as, drift velocity, W, D/? (ratio of diffusion coefficient to the mobility) and momentum transfer collision frequency ?m, for purpose of determination of magnetic drift velocity WM and magnetic deflection coefficient ? for low energy electrons, that moves in the electric field E, crossed with magnetic field B, i.e; E×B, in the nitrogen, Argon, Helium and it's gases mixtures as a function of: E/N (ratio of electric field strength to the number density of gas), E/P300 (ratio of electric field strength to the gas pressure) and D/? which covered a different ranges for E/P300 at temperatures 300°k (Kelvin). The results show
... Show MoreThe present research deal with ecological and geographical distribution of species and genera of Primulaceae in Iraq. The results were revealed that species distributed in the north , north-east and west of Iraq. Anagallis arvensis L. is the most prevalent species tolerant to different environmental conditions, while the species of Primula L. characterized as less widespread and limited in one District. In addition, the districts Rawanduz (MRO) and Sulaymaniyah (MSU) have ranked first in distribution of the species on geographical districts with (75%), while the districts southern desert (DSD) and Basra (LBA) in last place with (16.7%). Maps for geographical distribution for all species were illustrated.
Soil acts as a last sink for elements that people release into the environment through a range of activities due to its physiochemical characteristics. These substances, whether are organic or mineral pollutants, accumulate in the soil and constitute a significant risk to the ecosystem in general because they mess with the chemical and physical equilibrium of the soil, get into the food chain, and eventually get to people. When pollutant concentrations during the bioaccumulated process exceed the global standards for what is regarded as a contaminant in water, air, and soil. Nine soil samples were collected from different sites and two samples from each site at two depths (0-20 and 20-40 cm) to determine if there were any
... Show MoreSince oil is the primary source of vanadium in the environment and crude oil has a correspondingly high percentage of vanadium. Vanadium is crucial as a sign of oil contamination. Twenty soil samples were taken from various locations surrounding the East Baghdad oil field in Iraq during February 2022 and then analyzed to determine the effects of industrialization along with urbanization-related pollutants. The soil samples were analyzed using spectrophotometry analysis. In soil samples taken from the research area, vanadium concentrations range from (0.26 to 1.2 ppm). The contamination (CF), geoaccumulation (Igeo) and Enrichment factors (EF) indicated that all the soil samples are uncontaminated.