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.
Sildenafil, tadalafil, and vardenafil are phosphodiesterase type 5 enzyme (PDE-5) inhibitors used for the treatment of male erectile dysfunction. This present study aims to investigate 55 herbal products indicated for men’s sexual health from the Malaysian market for adulteration of PDE-5 inhibitors and analogues. The screening and identification of 20 PDE-5 inhibitors and analogues in herbal products of various forms (powder, capsules, tablets, and pastels) were conducted using gas chromatography–electron impact-mass spectrometer (GC-EI-MS). The analysis has shown that 19 herbal products were adulterated with PDE-5 inhibitors and analogues. Unique ion fragmentations and the presence of molecular
... Show MoreThe present paper agrees with estimation of scale parameter θ of the Inverted Gamma (IG) Distribution when the shape parameter α is known (α=1), bypreliminarytestsinglestage shrinkage estimators using suitable shrinkage weight factor and region. The expressions for the Bias, Mean Squared Error [MSE] for the proposed estimators are derived. Comparisons between the considered estimator with the usual estimator (MLE) and with the existing estimator are performed .The results are presented in attached tables.
s The study aims to identify the fairness in the distribution of municipal services between municipal districts and areas, from point of view of municipal chamber staff and from the point of view of the citizen. It also aims to identify factors affecting the fairness of the distribution of municipal services. Municipal services were being studied : hygiene and waste, water supply, sewer, creating gardens, and street paving .Factors which examined its impact on municipal services are: resources available to municipal chamber, the managerial process at municipal chamber, and factors in the external environment surrounding municipal chamber.The results of the study showed that level of the e
... Show MoreWeibull distribution is considered as one of the most widely distribution applied in real life, Its similar to normal distribution in the way of applications, it's also considered as one of the distributions that can applied in many fields such as industrial engineering to represent replaced and manufacturing time ,weather forecasting, and other scientific uses in reliability studies and survival function in medical and communication engineering fields.
In this paper, The scale parameter has been estimated for weibull distribution using Bayesian method based on Jeffery prior information as a first method , then enhanced by improving Jeffery prior information and then used as a se
... Show MoreIn this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of Bayes est
... Show MoreIn the present paper, the features of democratization of vocabulary in the language of mass media are tackled. Particularly, the functions of this phenomenon in the context of language as an ontological reality are analysed. As well, the growing role of the language of the media, and the language of politics as an integral part pertaining to it, is noted. Further, attention is paid to the excessive saturation of the language of the media along with the literary language, by means of evaluation which may include negative results.
In this concern, scholars had different views, specifically in relation to the use of colloquial vocabulary along with some vernacular profess
... Show MoreThermal performance of closed wet cooling tower has been investigated experimentally and theoretically
in this work. The theoretical model based on heat and mass transfer equations and heat and mass transfer balance equations which are established for steady state case. A new small indirect cooling tower was used for conducting experiments. The cooling capacity of cooling tower is 1 kW for an inlet water temperature of 38oC, a water mass velocity 2.3 kg/m2.s and an air wet bulb temperature of 26oC. This study investigates the relationship between saturation efficiency, cooling capacity and coefficient of performance of closed wet cooling tower versus different operating parameters such wet-bulb temperature, variable air-spray water fl
A reliability system of the multi-component stress-strength model R(s,k) will be considered in the present paper ,when the stress and strength are independent and non-identically distribution have the Exponentiated Family Distribution(FED) with the unknown shape parameter α and known scale parameter λ equal to two and parameter θ equal to three. Different estimation methods of R(s,k) were introduced corresponding to Maximum likelihood and Shrinkage estimators. Comparisons among the suggested estimators were prepared depending on simulation established on mean squared error (MSE) criteria.
This paper focuses on Load distribution factors for horizontally curved composite concrete-steel girder bridges. The finite-element analysis software“SAP2000” is used to examine the key parameters that can influence the distribution factors for horizontally curved composite steel
girders. A parametric study is conducted to study the load distribution characteristics of such bridge system due to dead loading and AASHTO truck loading using finite elements method. The key parameters considered in this study are: span-to-radius of curvature ratio, span length, number of girders, girders spacing, number of lanes, and truck loading conditions. The results have shown that the curvature is the most critical factor which plays an important
In this paper ,the problem of point estimation for the two parameters of logistic distribution has been investigated using simulation technique. The rank sampling set estimator method which is one of the Non_Baysian procedure and Lindley approximation estimator method which is one of the Baysian method were used to estimate the parameters of logistic distribution. Comparing between these two mentioned methods by employing mean square error measure and mean absolute percentage error measure .At last simulation technique used to generate many number of samples sizes to compare between these methods.