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 capacity factor is the main factor in assessing the efficiency of wind Turbine. This paper presents a procedure to find the optimal wind turbine for five different locations in Iraq based on finding the highest capacity factor of wind turbine for different locations. The wind data for twelve successive years (2009-2020) of five locations in Iraq are collected and analyzed. The longitudes and latitudes of the candidate sites are (44.3661o E, 33.3152o N), (47.7738o E, 30.5258o N), (45.8160o E, 32.5165o N), (44.33265o E, 32.0107o N) and (46.25691o E, 31.0510o N) for Baghdad, Basrah, Al-Kut, Al-Najaf, and Al-Nasiriyah respectively. The average wind velocity, standard deviation, Weibull shape and scale factors, and probability density functi
... Show MoreIn this paper, we introduce a new class of Weighted Rayleigh Distribution based on two parameters, one is the scale parameter and the other is the shape parameter introduced in Rayleigh distribution. The main properties of this class are derived and investigated . The moment method and least square method are used to obtain estimators of parameters of this distribution. The probability density function, survival function, cumulative distribution and hazard function are derived and found. Real data sets are collected to investigate two methods that depend on in this study. A comparison is made between two methods of estimation and clarifies that MLE method is better than the OLS method by using the mea
... Show MoreAl Huweizah Marsh is considered as the largest marsh at the southern part of Iraq. About one third of the marsh is located within the Iranian territory. Iran began to construct earth dikes along the Iraqi-Iranian international borders to separate the Iranian part of the marsh. The electrical conductivity, EC, value was adopted to be the indicator for the water salinity within the marsh. A steady two-dimensional water quality routing model was implemented by using the RMA2 and RMA4 softwares within the SMS computer package to estimate the distribution of the
EC values within the marsh seasonally during the wet, moderate and dry water years. The EC distribution Patterns were estimated considering the expected two cases of the marsh futu
This paper includes a comparison between denoising techniques by using statistical approach, principal component analysis with local pixel grouping (PCA-LPG), this procedure is iterated second time to further improve the denoising performance, and other enhancement filters were used. Like adaptive Wiener low pass-filter to a grayscale image that has been degraded by constant power additive noise, based on statistics estimated from a local neighborhood of each pixel. Performs Median filter of the input noisy image, each output pixel contains the Median value in the M-by-N neighborhood around the corresponding pixel in the input image, Gaussian low pass-filter and Order-statistic filter also be used.
Experimental results shows LPG-
... Show MoreA taxonomic keys was established of book and bark lice Order Psocoptera to isolated insects in Iraq from different localities of Baghdad and Babylon provinces. Thirteen species belong to eight genera and five families have been studied and described in details, these species were recorded for the first time in Iraq. These species are: Belaphopsocus badonneli New, 1971; Belaphotroctes oculeris Bodonnel, 1973; Embodopsocosis newi Bodonnel, 1973; Epipsocus stigamaticus Mockeord, 1991; Lepinotus huoni Schmidt and New, 2008; Liposcelies decolor Peramane 1925 Liposcelies paeta Pearman 1942 Liposclies bostrychphila Badonnel 1931; Liposclies brunnea Mostchulsky 1852; Liposclies entoophila Enderlein 1907; Neopsocopsis minuscule Li 2002 ;
... Show MoreIn this work, electron number density calculated using Matlab program code with the writing algorithm of the program. Electron density was calculated using Anisimov model in a vacuum environment. The effect of spatial coordinates on the electron density was investigated in this study. It was found that the Z axis distance direction affects the electron number density (ne). There are many processes such as excitation; ionization and recombination within the plasma that possible affect the density of electrons. The results show that as Z axis distance increases electron number density decreases because of the recombination of electrons and ions at large distances from the target and the loss of thermal energy of the electrons in
... Show MoreThe biggest problem of structural materials for fusion reactor is the damage caused by the fusion product neutrons to the structural material. If this problem is overcomed, an important milestone will be left behind in fusion energy. One of the important problems of the structural material is that nuclei forming the structural material interacting with fusion neutrons are transmuted to stable or radioactive nuclei via (n, x) (x; alpha, proton, gamma etc.) reactions. In particular, the concentration of helium gas in the structural material increases through deuteron- tritium (D-T) and (n, α) reactions, and this increase significantly changes the microstructure and the properties of the structural materials. T
... Show MoreBiodiesel define as the mono-alkyl esters of vegetable oil and animal fats is an alternative diesel fuel that is steadily gaining attention because the combustion of fossil fuels such as coal, oil and natural gas has been identify as a major cause of the increase in the concentration of carbon dioxide in the earth’s atmosphere and causing global warming.
The present work concerns with estimating the physical properties experimentally such as kinematic viscosity, density, flash point and carbon residue of biodiesel that produced by the esterification reaction of methanol and oleic acid with homogeneous catalysts H2SO4 in a lab-scale packed reactive distillation column using the best operating conditions of methanol to oleic acid 8:1,
In the present work, the effect of size of zinc dust particles on
AC argon discharge characteristics are investigated
experimentally. The plasma characteristics are determined by
using optical emission spectroscopy (OES) techniques. The
results illustrated that the electron temperature (Te) in the present
and absent of Zinc dust particle is reduced with increasing of
pressure. The electron temperature decreases with increasing of
Zinc dust size. Excitation temperature Tex is reduces with
increasing of Ar pressure in present and absent of zinc dust
particles. The present of Zinc dust reduce the Tex of Ar in both
Zinc dust size. The electron density increasing in the present and
absent of both zinc dust siz
The partial level density PLD of pre-equilibrium reactions that are described by Ericson’s formula has been studied using different formulae of single particle level density . The parameter was used from the equidistant spacing model (ESM) model and the non- equidistant spacing model (non-ESM) and another formula of are derived from the relation between and level density parameter . The formulae used to derive are the Roher formula, Egidy formula, Yukawa formula, and Thomas –Fermi formula. The partial level density results that depend on from the Thomas-Fermi formula show a good agreement with the experimental data.