doi:10.30526/34.3.2680

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Publication Date

Sun Aug 01 2021

Journal Name

Ibn Al-haitham Journal For Pure And Applied Sciences

Volume

34

Issue Number

3

DOI

10.30526/34.3.2680

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Robust Tests for the Mean Difference in Paired Data by Using Bootstrap Resampling Technique

Paired t-test

Robust

Bootstrap

Wilcoxon signed-rank test

Bivariate contaminated normal distribution

Bivariate Exponential.

Ghufran A.

Huda A.

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The paired sample t-test for testing the difference between two means in paired data is not robust against the violation of the normality assumption. In this paper, some alternative robust tests have been suggested by using the bootstrap method in addition to combining the bootstrap method with the W.M test. Monte Carlo simulation experiments were employed to study the performance of the test statistics of each of these three tests depending on type one error rates and the power rates of the test statistics. The three tests have been applied on different sample sizes generated from three distributions represented by Bivariate normal distribution, Bivariate contaminated normal distribution, and the Bivariate Exponential distribution.

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Publication Date

Sun Jun 20 2021

Journal Name

Baghdad Science Journal

Comparison of Some of Estimation methods of Stress-Strength Model: R = P(Y < X < Z)

Stress-Strength Model

Inverse Rayleigh Distribution

Least Square Estimator

Maximum Likelihood Method Estimator

Moment method

Uniformly Minimum Variance Unbiased Method

Shrinkage Methods.

Sairan Hamza

Bayda Atiya

Abbas Najim

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In this study, the stress-strength model R = P(Y < X < Z) is discussed as an important parts of reliability system by assuming that the random variables follow Invers Rayleigh Distribution. Some traditional estimation methods are used to estimate the parameters namely; Maximum Likelihood, Moment method, and Uniformly Minimum Variance Unbiased estimator and Shrinkage estimator using three types of shrinkage weight factors. As well as, Monte Carlo simulation are used to compare the estimation methods based on mean squared error criteria.

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Publication Date

Thu Dec 30 2021

Journal Name

Iraqi Journal Of Science

Gompertz Fréchet stress-strength Reliability Estimation

Reliability

Stress- Strength

Gompertz Fréchet Distribution

Maximum Likelihood Estimator

Least square Estimator

Weighted Least square Estimator

Regression Estimator

Ranked set sampling estimator

Sarah A.

Nada S.

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In this paper, the reliability of the stress-strength model is derived for probability P(Y<X) of a component having its strength X exposed to one independent stress Y, when X and Y are following Gompertz Fréchet distribution with unknown shape parameters and known parameters . Different methods were used to estimate reliability R and Gompertz Fréchet distribution parameters, which are maximum likelihood, least square, weighted least square, regression, and ranked set sampling. Also, a comparison of these estimators was made by a simulation study based on mean square error (MSE) criteria. The comparison confirms that the performance of the maximum likelihood estimator is better than that of the other estimators.

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(4)

Publication Date

Sun Oct 02 2022

Journal Name

Al-manhaj

Mathematical Statistics - Second Edition

Mathematical Expectation

Moment Generating Function

Cumulative Distribution Function

Probability Mass Function

Probability Density Function

Discrete Distributions

Continuous Distributions

Joint distributions

Marginal Distributions

Conditional Distributions

Transformations

Order Statistics.

Omar Abdulmohsin

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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, Neg

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Publication Date

Fri Mar 01 2019

Journal Name

Applied Acoustics

Theoretical model of absorption coefficient of an inhomogeneous MPP absorber with multi-cavity depths

Micro-perforated panel (MPP) absorber has been known as an alternative absorber to classical porous material given its facile installation

long durability

environmental friendliness and attractive appearance. Extensive studies of MPP absorber proposing the improvement of its absorption frequency bandwidth have been published. This study presents a MPP absorber introduced with inhomogeneous perforations and with multi-cavity depths. The MPP is divided into two sub-area

where each area has different hole diameter

perforation ratio and a separated backed cavity depth. The acoustic impedance is modelled using electrical equivalent circuit and the absorption coefficient is calculated under normal-incidence of sound. It is found that the inhomogeneous MPP can have good bandwidth of absorption by designing the sub-MPP of smaller perforation ratio with large hole diameter and the one having the larger perforation ratio with smaller hole diameter. The absorption bandwidth can be conveniently controlled by adjusting the cavity depth of each sub-MPP. The results from the experimental work show good agreement with the theoretical model.

Ali Ibrahim

Azma

Roszaidi

Iwan

Al-Ameri

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Publication Date

Sat Sep 01 2018

Journal Name

Polyhedron

Novel dichloro (bis {2-[1-(4-methylphenyl)-1H-1, 2, 3-triazol-4-yl-κN3] pyridine-κN}) metal (II) coordination compounds of seven transition metals (Mn, Fe, Co, Ni, Cu, Zn and Cd)

The 1

3-dipolar cycloaddition “click” reaction between an azide and an alkyne to give a 1

2

3-triazole was reported by Huisgen in 1961 [1]. In 2002 the Copper(I)-catalyzed Azide-Alkyne Cycloaddition (CuAAC) to prepare a 1

2

3-triazole was reported [2]

[3]. The existence of relatively basic nitrogen atoms in the 1

2

3-triazole rings

and the possibility of introducing additional donor groups in the substituents (Fig. 1)

made the CuAAC “click” reaction an attractive method to prepare differently substituted 1

2

3-triazoles. These compounds have been used as ligands to coordinate to various metal ions that display a range of applications such as in electrochemical and photochemical studies

in supramolecular chemistry

magnetism

metal-ion sensing and catalysis [4]. The reasons for the success of the “click” reaction

is that it is easy to carry out and is widely applicable. It is not affected by a variety of functional groups

and can be carried out with a variety of Cu(I) catalysts and solvents

including aqueous conditions. The Cu(I) catalysts overcome the high activation energy barrier of the non-catalyzed Huisgen reaction by changing the mechanism of the reaction. A large variety of copper catalysts can be used for the CuAAC reaction

on condition that the maximum concentration of Cu(I) species is generated during the reaction. The pre-catalyst can be a Cu(II) salt (usually CuSO4) together with a reducing agent (often sodium ascorbate) or a Cu(I) compound in the presence of a base or amine ligand and a reducing agent to prevent oxidation to Cu(II). Some strong oxidising cupric salts or complexes such as Cu(OAc)2 also work. The solvent is very flexible from organic to aqueous

with the most commonly used combination water + an alcohol (t-BuOH

MeOH or EtOH). The key role of the solvent or solvent mixture is to solubilize the substrates and Cu(I) catalyst in order to ensure rapid reactions. Such aqueous conditions are very useful for biochemical conjugations

as well as for organic syntheses. We recently reported on the synthesis of a series of differently substituted 1

2

3-triazole chromophores

the substituted 2-(1-phenyl-1H-1

2

3-triazol-4-yl)pyridine ligands [5]

see Fig. 2 middle

with substituents R = H (L1)

CH3 (L2)

OCH3 (L3)

COOH

F

Cl

CN

CF3

O(CH2)3CH3 and N(CH3)2. These versatile ligands were found to coordinate to various first row transition metals

such as manganese

cobalt and nickel [6]. Here we extend the series to include more first row transition metal(II) coordination compounds

iron

copper and zinc

as well as a second row transition metal(II) coordination compound

cadmium

containing the 2-(1-(4-methyl-phenyl)-1H-1

2

3-triazol-1-yl)pyridine chromophore (Fig. 2 right with R = CH3). This series of seven novel coordination compounds is the first series of pyridyl-triazole based transition metal coordination compounds where seven different transition metals are coordinated to the same 1

2

3-triazole chromophore

namely 2-(1-(4-methyl-phenyl)-1H-1

2

3-triazol-1-yl)pyridine.

Kinaan M

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