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On exponential and other random variable generators

Annals of the Institute of Statistical Mathematics 1961年第1期13.0卷 231-237页

作者： Sibuya, Masaaki The Institute of Statistical Mathematics United States

G. Marsaglia [6] proposed a new method for generating exponential random variables. In this note, his method is modified and generalized for generating χ2 random variables with even degrees of freedom. Remarks refer ... 详细信息

G. Marsaglia [6] proposed a new method for generating exponential random variables. In this note, his method is modified and generalized for generating χ² random variables with even degrees of freedom. Remarks refer to general χ² and normal random variable generators. © 1961 Institute of Statistical Mathematics.

关键词： Machine Time exponential random variable Uniform random Number Float Point Arithmetic Uniform random variable

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An Improved Compound Gaussian Model for Bivariate Surface EMG Signals Related to Strength Training

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IEEE TRANSACTIONS ON HUMAN-MACHINE SYSTEMS 2025年第1期55卷 58-70页

作者： Kusuru, Durgesh Turlapaty, Anish C. Thakur, Mainak Indian Inst Informat Technol Sri City Biosignal Anal Grp Chittoor 517646 Andhra Pradesh India

Recent literature suggests that the surface electromyography (sEMG) signals have nonstationary statistical characteristics, specifically due to the random nature of the covariance. Thus, the suitability of a statistical model for sEMG signals is determined by the choice of an appropriate model for describing the covariance. The purpose of this study is to propose a compound-Gaussian (CG) model for multivariate sEMG signals in which the latent variable of covariance is modeled as a random variable that follows an exponential model. The parameters of the model are estimated using the iterative expectation maximization (EM) algorithm. Further, a new dataset, electromyography analysis of human activities database 2 (EMAHA-DB2), is developed. The proposed model is evaluated through both qualitative and quantitative methods. Based on the model fitting analysis on the sEMG signals from EMAHA-DB2, it is found that the proposed CG model fits more closely to the empirical pdf of sEMG signals than the existing models. In addition, statistical analyses are carried out among the models and estimated parameters under different scenarios. The estimate of the exponential model's rate parameter exhibits a clear relationship with training weights, potentially correlating with underlying motor unit activity. Finally, the average signal power estimates of the channels show distinctive dependency on the training weights, the subject's training experience, and the type of activity.

关键词： Compound Gaussian (CG) models expectation maximization (EM) algorithm exponential random variable surface electromyography (sEMG)

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Probabilistic linear programming problems with exponential random variables: A technical note

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1998年第3期111卷 589-597页

作者： Biswal, MP Biswal, NP Li, DA Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India Chinese Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Peoples R China

A method for solving probabilistic linear programming problems with exponential random variables is presented in this paper. Assuming that either some or all of the parameters are exponential random variables a transformation is presented to convert the probabilistic linear programming problem to a deterministic mathematical programming problem. A non-linear programming algorithm can then be used to solve the resulting deterministic problem. (C) 1998 Elsevier Science B.V. All rights reserved.

关键词： probabilistic linear programming exponential random variable probability density function non-linear programming

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Stochastic orders of the sums of two exponential random variables

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STATISTICS & PROBABILITY LETTERS 2001年第4期51卷 389-396页

作者： Chang, KH Chung Yuan Christian Univ Dept Ind Engn Chungli 320 Taiwan

The sums of two exponential random variables are compared in the sense of likelihood ratio order. It is shown that, under some conditions, their likelihood ratio order does not exist and, if it exists, the complete co... 详细信息

关键词： stochastic ordering likelihood ratio order exponential random variable sum of random variables

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Better Articulating Normal Curve Theory for Introductory Mathematical Statistics Students: Power Transformations and Their Back-Transformations

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AMERICAN STATISTICIAN 2013年第3期67卷 157-169页

作者： Griffith, Daniel A. Univ Texas Dallas Sch Econ Polit & Policy Sci Richardson TX 75080 USA

This article addresses a gap in many, if not all, introductory mathematical statistics textbooks, namely, transforming a random variable so that it better mimics a normal distribution. Virtually all such textbooks treat the subject of variable transformations, which furnishes a nice opportunity to introduce and study this transformation-to-normality topic, a topic students frequently encounter in subsequent applied statistics courses. Accordingly, this article reviews variable power transformations of the Box-Cox type within the context of normal curve theory, as well as addresses their corresponding back-transformations. It presents four theorems and a conjecture that furnish the basics needed to derive equivalent results for all nonnegative values of the Box-Cox power transformation exponent. Results are illustrated with the exponential random variable. This article also includes selected pedagogic tools created with R code.

关键词： Box-Cox power transformation exponential random variable Normality R

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FURTHER CONSIDERATION ON NORMAL random variable GENERATOR

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 1962年第2期14卷 159-165页

作者： SIBUYA, M The Institute of Statistical Mathematics USA

In a previous paper [3] the author considered a computer technique for generating exponential random variables and its applications to the generation of random variables of other types. He suggested to combine the new exponential random variable generator with J. C. Butcher’s method [1] to get normal random deviates. In this note, an improvement of the idea is shown with a remark on the rejection technique in the Monte Carlo method.

关键词： Probability Density Function exponential random variable Scheme Procedure Uniform random variable Poisson random variable

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On the Correlation Structure of exponential Order Statistics and Some Extensions

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MATHEMATICAL METHODS OF STATISTICS 2016年第3期25卷 196-206页

作者： Hung, Y. C. Chen, R. W. Balakrishnan, N. Natl Chengchi Univ Dept Stat Taipei Taiwan Univ Miami Dept Math Coral Gables FL 33124 USA McMaster Univ Dept Math & Stat Hamilton ON Canada

In this paper, we carry out a theoretical study of the correlation coefficients between exponential order statistics and their monotonicity properties. Then, aided by a Monte Carlo simulation study, we make some conje... 详细信息

关键词： exponential random variable order statistics correlation coefficient continuous random variable

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A METHOD FOR GENERATING UNIFORMLY DISTRIBUTED POINTS ON N-DIMENSIONAL SPHERES

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 1962年第1期14卷 81-85页

作者： SIBUYA, M The Institute of Statistical Mathematics USA

In this note a computer procedure to transform uniform random variables into random points uniformly distributed on an N-dimensional sphere is presented. The procedure is much simpler than the ones thus far published.

关键词： random Point exponential random variable Uniform random variable Probability Density Func Dimensional Unit Sphere

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InterferenceAnalyzer: Tools for the analysis and simulation of multi-locus genetic data

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BMC BIOINFORMATICS 2005年第1期6卷 297-297页

作者： Viswanath, L Housworth, EA Indiana Univ Dept Math Bloomington IN 47405 USA Indiana Univ Sch Informat Bloomington IN 47405 USA Indiana Univ Dept Biol Bloomington IN 47405 USA

Background: Good statistical models for analyzing and simulating multilocus recombination data exist but are not accessible to many biologists because their use requires reasonably sophisticated mathematical and computational implementation. While some labs have direct access to statisticians or programmers competent to carry out such analyses, many labs do not. We have created a platform independent application with an easy-to-use graphical user interface that will carry out such analyses including the simulations needed to bootstrap confidence intervals for the parameters of interest. This software should make multi-locus techniques accessible to labs that previously relied on less powerful and potentially statistically confounded single interval or double interval techniques. Results: We introduce InterferenceAnalyzer, an implementation with a user-friendly graphical interface incorporating previously developed algorithms for the analysis and simulation of multilocus recombination data. We demonstrate the use and features of the program with an example of multilocus tetrad data from the mustard plant, Arabidopsis thaliana, and the yeast, Saccharomyces cerevisiae. Conclusion: InterferenceAnalyzer provides easy access to the powerful and appropriate statistical tools for the multi-locus analysis of genetic data.

关键词： Maximum Likelihood Estimator Extended Model Counting Model Likelihood Ratio Test Statistic exponential random variable

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Genetic Analysis Workshop 15: simulation of a complex genetic model for rheumatoid arthritis in nuclear families including a dense SNP map with linkage disequilibrium between marker loci and trait loci

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BMC proceedings 2007年第1期1 Suppl 1卷 S4页

作者： Michael B Miller Gregg R Lind Na Li Soon-Young Jang Division of Epidemiology and Community Health School of Public Health and Institute of Human Genetics University of Minnesota 1300 S Second Street Suite 300 Minneapolis Minnesota 55454 USA. mbmiller@taxa.epi.umn.edu

Data for Problem 3 of the Genetic Analysis Workshop 15 were generated by computer simulation in an attempt to mimic some of the genetic and epidemiological features of rheumatoid arthritis (RA) such as its population prevalence, sex ratio, risk to siblings of affected individuals, association with cigarette smoking, the strong effect of genotype in the HLA region and other genetic effects. A complex genetic model including epistasis and genotype-by-environment interaction was applied to a population of 1.9 million nuclear families of size four from which we selected 1500 families with both offspring affected and 2000 unrelated, unaffected individuals all of whose first-degree relatives were unaffected. This process was repeated to produce 100 replicate data sets. In addition, we generated marker data for 22 autosomes consisting of a genome-wide set of 730 simulated STRP markers, 9187 SNP markers and an additional 17,820 SNP markers on chromosome 6. Appropriate linkage disequilibrium between markers and between trait loci and markers was modelled using HapMap Phase 1 data http://***/downloads/phasing/2005-03_phaseI/. The code base for this project was written primarily in the Octave programming language, but it is being ported to the R language and developed into a larger project for general genetic simulation called GenetSim http://***/. All of the source code that was used to generate the GAW 15 Problem 3 data is freely available for download at http://***/gaw15/.

关键词： Rheumatoid Arthritis Marker Data Genetic Analysis Workshop exponential random variable Shared Environment Effect

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