Confidence Bounds and Hypothesis Tests for Normal Distribution Coefficients of Variation PDF Download
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Author: S. P. Verrill
Publisher:
ISBN:
Category : Confidence intervals
Languages : en
Pages : 60
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Book Description
For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations. To develop these confidence bounds and test, we first establish that estimators based on Newton steps from [the square root of n]-consistent estimators may be used in place of efficient solutions of the likelihood equations in likelihood ratio, Wald, and Rao tests. Taking a quadratic mean differentiability approach, Lehmann and Romano have outlined proofs of similar results. We take a Cramér condition approach and make the conditions and their use explicit. Keywords: coefficient of variation, signal to noise ratio, risk to return ratio, one-step Newton estimators, Newton's method, [the square root of n]-consistent estimators, efficient likelihood estimators, Cramér conditions, quadratic mean differentiability, likelihood ratio test, Wald test, Rao test, asymptotics.
Author: S. P. Verrill
Publisher:
ISBN:
Category : Confidence intervals
Languages : en
Pages : 60
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Book Description
For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations. To develop these confidence bounds and test, we first establish that estimators based on Newton steps from [the square root of n]-consistent estimators may be used in place of efficient solutions of the likelihood equations in likelihood ratio, Wald, and Rao tests. Taking a quadratic mean differentiability approach, Lehmann and Romano have outlined proofs of similar results. We take a Cramér condition approach and make the conditions and their use explicit. Keywords: coefficient of variation, signal to noise ratio, risk to return ratio, one-step Newton estimators, Newton's method, [the square root of n]-consistent estimators, efficient likelihood estimators, Cramér conditions, quadratic mean differentiability, likelihood ratio test, Wald test, Rao test, asymptotics.
Author: United States Department of Agriculture
Publisher: CreateSpace
ISBN: 9781508446224
Category :
Languages : en
Pages : 60
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Book Description
For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations.
Author:
Publisher:
ISBN:
Category : Confidence intervals
Languages : en
Pages : 57
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Book Description
Author: Rubing Luo
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Approximation of con dence interval and hypothesis testing for a normal mean when the coe cient of variation is known, is quite di erent from the situation when the variance is known. Mostly, the situation when the variance is known is only of theoretical interest. There are many practical situations when the coe cient of variation is known. This situation arises in medical, biological and environmental studies. In the theoretical part of the thesis, we proved that the considered estimates are unbiased estimator with minimum variance and asymptotically normal. We con- struct statistical tests for the normal mean based on the best asymptotically normal estimator with minimum variance and the minimum risk scale equivariant estimator and the modi ed version of them. In the computational part, we calculate the cov- erage probability and width length of con dence interval of ve estimators. We also develop hypothesis tests for normal mean in case of known coe cient of variation. We estimate the type I error and the power of the proposed statistics under di er- ent situations. The simulation results show that all proposed test statistics perform better for a large sample and a small value of coe cient of variation. Keywords: Mean of a normal distribution; Coe cient of variation; Coverage probability; Con dence interval; Hypothesis testing.
Author: Alexander Holmes
Publisher:
ISBN: 9781998109487
Category :
Languages : en
Pages : 0
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Book Description
Printed in b&w. Introductory Business Statistics is designed to meet the scope and sequence requirements of the one-semester statistics course for business, economics, and related majors. Core statistical concepts and skills have been augmented with practical business examples, scenarios, and exercises. The result is a meaningful understanding of the discipline, which will serve students in their business careers and real-world experiences.
Author: J.S. Maritz
Publisher: CRC Press
ISBN: 1000153002
Category : Mathematics
Languages : en
Pages : 279
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Book Description
Distribution-free statistical methods enable users to make statistical inferences with minimum assumptions about the population in question. They are widely used, especially in the areas of medical and psychological research. This new edition is aimed at senior undergraduate and graduate level. It also includes a discussion of new techniques that have arisen as a result of improvements in statistical computing. Interest in estimation techniques has particularly grown, and this section of the book has been expanded accordingly. Finally, Distribution-Free Statistical Methods includes more examples with actual data sets appearing in the text.
Author: Arnold Naiman
Publisher: McGraw-Hill Science, Engineering & Mathematics
ISBN:
Category : Mathematics
Languages : en
Pages : 328
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Book Description
Common statitical measures; The histogram; Probability; The binomial distribution; The normal distribution; Approximation of the binomial distribution by use of the normal distribution; Hypothesis testing: binomial one-sample; Hypothesis testing: binomial two-sample; Hypothesis testing with sample means: large samples; Hypothesis testing with sample means: small samples; Confidence intervals; A chi-square test; Correlation and prediction; Tests involving variance; Nonparametric tests.
Author: Walter Clark Hamilton
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 248
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Book Description
Author: Jerrold H. Zar
Publisher:
ISBN: 9781292024042
Category : Biometry
Languages : en
Pages : 756
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Book Description
Zar's Biostatistncal Analysis, Fifth Edition, is the ideal textbook for graduate and undergraduate students seeking practncal coverage of statistncal analysis methods used by researchers to collect, summarize, analyze and draw conclusnons from biologic E research. The latest editnon of this best-selling textbook is both comprehensive and easy to read. It is suitable as an introductnon for begnnnnng students and as a comprehensive reference book for biologic E researchers and for advanced students. This book is appropriate for a one- or two-semester, junior or graduate-level course in biostatistncs, biometry, quantitatnve biology, or statistics, and assumes a prerequisite ofalgebra.
Author: Chester Ismay
Publisher: CRC Press
ISBN: 1000763463
Category : Mathematics
Languages : en
Pages : 461
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Book Description
Statistical Inference via Data Science: A ModernDive into R and the Tidyverse provides a pathway for learning about statistical inference using data science tools widely used in industry, academia, and government. It introduces the tidyverse suite of R packages, including the ggplot2 package for data visualization, and the dplyr package for data wrangling. After equipping readers with just enough of these data science tools to perform effective exploratory data analyses, the book covers traditional introductory statistics topics like confidence intervals, hypothesis testing, and multiple regression modeling, while focusing on visualization throughout. Features: ● Assumes minimal prerequisites, notably, no prior calculus nor coding experience ● Motivates theory using real-world data, including all domestic flights leaving New York City in 2013, the Gapminder project, and the data journalism website, FiveThirtyEight.com ● Centers on simulation-based approaches to statistical inference rather than mathematical formulas ● Uses the infer package for "tidy" and transparent statistical inference to construct confidence intervals and conduct hypothesis tests via the bootstrap and permutation methods ● Provides all code and output embedded directly in the text; also available in the online version at moderndive.com This book is intended for individuals who would like to simultaneously start developing their data science toolbox and start learning about the inferential and modeling tools used in much of modern-day research. The book can be used in methods and data science courses and first courses in statistics, at both the undergraduate and graduate levels.
