Maxwell–Boltzmann distribution curves
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Abstract. This article aims to investigate the computational distribution of neutron flux using. Maxwell-Boltzmann statistics. The reactor geometry used is
Some Estimators the Parameter of Maxwell- Boltzmann Distribution
The statistical mechanics deal with Maxwell-Boltzmann distribution which description the energy and velocity in gas when the molecules motion freely between.
In this exercise you will use Excel to create a spreadsheet for the
Molecules at any given temperature do not all have the same speed but in fact a distribution of speeds given by the Maxwell-Boltzmann distribution.
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Scottish physicist James Clerk Maxwell developed his kinetic theory of gases in 1859 Maxwell determined the distribution of velocities among the molecules
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[PDF] 1 Maxwell-Boltzmann distribution function Masatsugu Sei - bingweb
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[PDF] The Maxwell-Boltzmann Distribution - TSFX
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PDF A derivation of the Maxwell-Boltzmann distribution based on cominatorics of distinguishable particles suitable for a basic physics course
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6 jui 2022 · In this section we review the basic assumptions on which Maxwell- Boltzmann built his statistical distribution
Global Journal of Pure and Applied Mathematics.
ISSN 0973-1768 Volume 13, Number 10 (2017), pp. 7211-7227© Research India Publications
http://www.ripublication.comSome Estimators the Parameter of Maxwell-
Boltzmann Distribution
Iden H. Alkanani* and Shayma G. Salman**
*University of Baghdad, College of Science for Women Dept: Mathematics, Jadriah Bridge Street AljadriahBaghdad-00964, Iraq.
E-mail: Iden_Alkanani@yahoo.com
**University of Baghdad,College of Science for Women, Mathematics
739 Alameen 2, Baghdad-00964, Baghdad, Iraq.
E-mail: shgs.baghdad@gmail.com
Abstract
In this paper, the problem of point estimation for the one parameter ߠ Maxwell-Boltzmann distribution has been investigated using simulation technique, to estimate the parameter of Maxwell-Boltzmann by many methods. These methods are divided in two sections; the first section includes Non-Bayesian statistical methods, such as minimum variance unbiased estimator method, while the second section includes Bayesian statistical methods, such as (extension Jeffrey Bayesian estimator, standard Bayesian informative prior Method, and Shrinkage Method). Comparing between these four mentioned methods by employing mean square error measure. At last simulation technique used to generate many number of samples sizes to compare between these methods. Keywords: Maxwell-Boltzmann distribution, Minimum Variance Unbiased Method, Extension Jeffrey Bayesian Method, Informative Bayesian prior Method, Shrinkage Method, Mean square error, simulation technique.7212 Iden H. Alkanani and Shayma G. Salman
1. INTRODUCTION:
The statistical mechanics deal with Maxwell-Boltzmann distribution which description the energy and velocity in gas, when the molecules motion freely between the levels of energy, and do not interaction with each other, as employment of the temperature of gas system. In the statistical mechanics, the Maxwell-Boltzmann distribution grant the velocity and energy in gas. In the statistical mechanics, the Maxwell-Boltzmann distribution grant the velocity and energy molecules in thermal equilibrium. In (1989) Tyagi and Bhattacherya introduction the Maxwell distribution in lifetime model [1]. In (1998) Chaturvedi and Rani used classical and Bayesian method of the generalized Maxwell distribution in lifetime to found the reliability estimation function [2]. In (2005) Bekker and Roux made the characteristic of reliability function in Maxwell distribution and estimate the Bayesian as study [3]. In (2009) krishna and Malik estimated the reliability function in Maxwell distribution by using type-two censored sample [4]. In (2011) Kasmi, and others utilizing the maximum likelihood estimator in type one censored sample of mixture Maxwell distribution [5]. In (2012) Kasmi and others utilizing the Bayesian estimation for two component of Maxwell distribution by using type-one censored sample [6]. In (2013) Al-Baldawi compare between some Bayesian estimator with maximum likelihood estimator for Maxwell distribution using non-informative priors [7]. In (2016) Rasheed and Khalifa estimated the parameter of Maxwell distribution by using Bayes estimator under quadratic loss function usingNon-informative prior [8].
The aim of this paper is to study four estimation methods, the first is minimum variance unbiased estimator method, the second is extension Jeffrey Bayesian estimator method, the third is informative Bayesian prior estimator method, the fourth is Shrinkage estimator method, then compare between them by using Mean Square Error (MSE) utilizing Monte Carlo simulation technique with various sample sizes.2. MAXWELL-BOLTZMANN DISTRIBUTION.
parameter, it has the following cumulative distribution function (cdf): Some Estimators the Parameter of Maxwell-Boltzmann Distribution 7213Where ߛ
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The probability density function (pdf) for the Maxwell-Boltzmann distribution defined as follows:݂:Tquotesdbs_dbs21.pdfusesText_27
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