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Exact Statistical Inferences for Functions of Parameters of the Log-Gamma Distribution
UNLV Theses, Dissertations, Professional Papers, and Capstones 5-1-2015 Exact Statistical Inferences for Functions of Parameters of the Log-Gamma Distribution Joseph F. Mcdonald University of Nevada, Las Vegas Follow this and additional works at: https://digitalscholarship.unlv.edu/thesesdissertations Part of the Multivariate Analysis Commons, and the Probability Commons Repository Citation Mcdonald, Joseph F., "Exact Statistical Inferences for Functions of Parameters of the Log-Gamma Distribution" (2015). UNLV Theses, Dissertations, Professional Papers, and Capstones. 2384. http://dx.doi.org/10.34917/7645961 This Dissertation is protected by copyright and/or related rights. It has been brought to you by Digital Scholarship@UNLV with permission from the rights-holder(s). You are free to use this Dissertation in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/or on the work itself. This Dissertation has been accepted for inclusion in UNLV Theses, Dissertations, Professional Papers, and Capstones by an authorized administrator of Digital Scholarship@UNLV. For more information, please contact [email protected]. EXACT STATISTICAL INFERENCES FOR FUNCTIONS OF PARAMETERS OF THE LOG-GAMMA DISTRIBUTION by Joseph F. McDonald Bachelor of Science in Secondary Education University of Nevada, Las Vegas 1991 Master of Science in Mathematics University of Nevada, Las Vegas 1993 A dissertation submitted in partial fulfillment of the requirements for the Doctor of Philosophy - Mathematical Sciences Department of Mathematical Sciences College of Sciences The Graduate College University of Nevada, Las Vegas May 2015 We recommend the dissertation prepared under our supervision by Joseph F. -
IBM SPSS Exact Tests
IBM SPSS Exact Tests Cyrus R. Mehta and Nitin R. Patel Note: Before using this information and the product it supports, read the general information under Notices on page 213. This edition applies to IBM® SPSS® Exact Tests 21 and to all subsequent releases and modifications until otherwise indicated in new editions. Microsoft product screenshots reproduced with permission from Microsoft Corporation. Licensed Materials - Property of IBM © Copyright IBM Corp. 1989, 2012. U.S. Government Users Restricted Rights - Use, duplication or disclosure restricted by GSA ADP Schedule Contract with IBM Corp. Preface Exact Tests™ is a statistical package for analyzing continuous or categorical data by exact methods. The goal in Exact Tests is to enable you to make reliable inferences when your data are small, sparse, heavily tied, or unbalanced and the validity of the corresponding large sample theory is in doubt. This is achieved by computing exact p values for a very wide class of hypothesis tests, including one-, two-, and K- sample tests, tests for unordered and ordered categorical data, and tests for measures of asso- ciation. The statistical methodology underlying these exact tests is well established in the statistical literature and may be regarded as a natural generalization of Fisher’s ex- act test for the single 22× contingency table. It is fully explained in this user manual. The real challenge has been to make this methodology operational through software development. Historically, this has been a difficult task because the computational de- mands imposed by the exact methods are rather severe. We and our colleagues at the Harvard School of Public Health have worked on these computational problems for over a decade and have developed exact and Monte Carlo algorithms to solve them. -
The NPAR1WAY Procedure This Document Is an Individual Chapter from SAS/STAT® 14.1 User’S Guide
SAS/STAT® 14.1 User’s Guide The NPAR1WAY Procedure This document is an individual chapter from SAS/STAT® 14.1 User’s Guide. The correct bibliographic citation for this manual is as follows: SAS Institute Inc. 2015. SAS/STAT® 14.1 User’s Guide. Cary, NC: SAS Institute Inc. SAS/STAT® 14.1 User’s Guide Copyright © 2015, SAS Institute Inc., Cary, NC, USA All Rights Reserved. Produced in the United States of America. For a hard-copy book: No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the publisher, SAS Institute Inc. For a web download or e-book: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. The scanning, uploading, and distribution of this book via the Internet or any other means without the permission of the publisher is illegal and punishable by law. Please purchase only authorized electronic editions and do not participate in or encourage electronic piracy of copyrighted materials. Your support of others’ rights is appreciated. U.S. Government License Rights; Restricted Rights: The Software and its documentation is commercial computer software developed at private expense and is provided with RESTRICTED RIGHTS to the United States Government. Use, duplication, or disclosure of the Software by the United States Government is subject to the license terms of this Agreement pursuant to, as applicable, FAR 12.212, DFAR 227.7202-1(a), DFAR 227.7202-3(a), and DFAR 227.7202-4, and, to the extent required under U.S. -
Statistical Inferences for Functions of Parameters of Several Pareto and Exponential Populations with Application in Data Traffic
UNLV Theses, Dissertations, Professional Papers, and Capstones 2009 Statistical inferences for functions of parameters of several pareto and exponential populations with application in data traffic Sumith Gunasekera University of Nevada Las Vegas Follow this and additional works at: https://digitalscholarship.unlv.edu/thesesdissertations Part of the Applied Mathematics Commons, Applied Statistics Commons, and the Statistical Methodology Commons Repository Citation Gunasekera, Sumith, "Statistical inferences for functions of parameters of several pareto and exponential populations with application in data traffic" (2009). UNLV Theses, Dissertations, Professional Papers, and Capstones. 46. http://dx.doi.org/10.34917/1363595 This Dissertation is protected by copyright and/or related rights. It has been brought to you by Digital Scholarship@UNLV with permission from the rights-holder(s). You are free to use this Dissertation in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/or on the work itself. This Dissertation has been accepted for inclusion in UNLV Theses, Dissertations, Professional Papers, and Capstones by an authorized administrator of Digital Scholarship@UNLV. For more information, please contact [email protected]. STATISTICAL INFERENCES FOR FUNCTIONS OF PARAMETERS OF SEVERAL PARETO AND EXPONENTIAL POPULATIONS WITH APPLICATIONS IN DATA TRAFFIC by Sumith Gunasekera Bachelor of Science University of Colombo, Sri Lanka 1995 A dissertation submitted in partial fulfillment of the requirements for the Doctor of Philosophy Degree in Mathematical Sciences Department of Mathematical Sciences College of Sciences Graduate College University of Nevada, Las Vegas August 2009 . -
PASW Exact Tests
Exact Tests ™ Cyrus R. Mehta and Nitin R. Patel For more information about SPSS® software products, please visit our WWW site at http://www.spss.com or contact Marketing Department SPSS Inc. 233 South Wacker Drive, 11th Floor Chicago, IL 60606-6307 Tel: (312) 651-3000 Fax: (312) 651-3668 SPSS is a registered trademark. PASW is a registered trademark of SPSS Inc. The SOFTWARE and documentation are provided with RESTRICTED RIGHTS. Use, duplication, or disclosure by the Government is subject to restrictions as set forth in subdivision (c)(1)(ii) of The Rights in Technical Data and Computer Software clause at 52.227-7013. Contractor/manufacturer is SPSS Inc., 233 South Wacker Drive, 11th Floor, Chicago, IL, 60606-6307. General notice: Other product names mentioned herein are used for identification purposes only and may be trademarks of their respective companies. TableLook is a trademark of SPSS Inc. Windows is a registered trademark of Microsoft Corporation. Printed in the United States of America. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Preface Exact Tests is a statistical package for analyzing continuous or categorical data by ex- act methods. The goal in Exact Tests is to enable you to make reliable inferences when your data are small, sparse, heavily tied, or unbalanced and the validity of the corre- sponding large sample theory is in doubt. This is achieved by computing exact p values for a very wide class of hypothesis tests, including one-, two-, and K- sample tests, tests for unordered and ordered categorical data, and tests for measures of association. -
Exact Nonparametric Binary Choice and Ordinal Regression Analysis"
Exact Nonparametric Binary Choice and Ordinal Regression Analysis Karl H. Schlagy February 15, 2014 Abstract We provide methods for investigating the relationship between an attribute and an ordinal outcome, as in a binary choice model. We do not make additional assumptions on the errors as in the (ordinal) logit or probit models and do not invoke asymptotic theory. These tests are exact as their type I error probability can be bounded above by their nominal level in the data set that is being investigated. Bounds on type II error probabilities are provided. Methods extend to duration and survival analysis with right censoring. Several data applications are given. Keywords: exact, probit, logit, stochastic inequality, latent variable, single index model, ordinal, nonparametric, survival analysis. JEL classi…cation: C14, C20. 1 Introduction Binary choice models in the form of logistic or probit regressions are very popular for understanding how attributes in‡uence outcomes, yet they have grave drawbacks when coming to inference. When …nding signi…cant evidence of a coe¢ cient there may be several reasons why the corresponding null hypothesis has been rejected. One would wish that this reveals a signi…cant evidence of a positive relationship between this attribute and the outcome. However there are also three other reasons that can lead to a rejection of the null hypothesis. (i) Errors may not distributed as postulated by the underlying model. (ii) The formulae used to compute the corresponding p value We wish to thank Francesca Solmi whose work motivated this project, Heiko Rachinger for valuable comments and Robin Ristl for programming the software used to analyze the data. -
Exact Hypothesis Testing Without Assumptions & New and Old
Exact Hypothesis Testing without Assumptions - New and Old Results not only for Experimental Game Theory1 Karl H. Schlag October 11, 2013 1The author would like to thank Caterina Calsamiglia, Patrick Eozenou and Joel van der Weele for comments on exposition of an earlier version. 1 Contents 1 Introduction 1 2 When are T Tests Exact? 3 3 Two Independent Samples 4 3.1 Preliminaries ............................... 4 3.1.1 Documentation . 8 3.1.2 Accepting the Null Hypothesis . 9 3.1.3 Side Remarks on the P Value . 10 3.1.4 Evaluating Tests . 12 3.1.5 Ex-Post Power Analysis . 15 3.1.6 Con…dence Intervals . 16 3.1.7 Noninferiority Tests and Reversing a Test . 18 3.1.8 Estimation and Hypothesis Testing . 18 3.1.9 Substantial Signi…cance . 19 3.2 Binary-Valued Distributions . 19 3.2.1 One-Sided Hypotheses . 19 3.2.2 Tests of Equality . 24 3.3 Multi-Valued Distributions . 25 3.3.1 Identity of Two Distributions . 25 3.3.2 Stochastic Dominance . 28 3.3.3 Medians .............................. 29 3.3.4 Stochastic Inequalities and Categorical Data . 30 3.3.5 Means ............................... 32 3.3.6 Variances ............................. 36 4 Matched Pairs 36 4.1 Binary-Valued Distributions . 36 4.1.1 Comparing Probabilities . 36 4.1.2 Correlation . 37 4.2 Multi-Valued Distributions . 38 4.2.1 Identity of Two Marginal Distributions . 38 2 4.2.2 Independence of Two Distributions . 39 4.2.3 Stochastic Inequalities and Ordinal Data . 39 4.2.4 Means ............................... 40 4.2.5 Covariance and Correlation . -
PROC FREQ Statement
SAS/STAT® 13.1 User’s Guide The FREQ Procedure This document is an individual chapter from SAS/STAT® 13.1 User’s Guide. The correct bibliographic citation for the complete manual is as follows: SAS Institute Inc. 2013. SAS/STAT® 13.1 User’s Guide. Cary, NC: SAS Institute Inc. Copyright © 2013, SAS Institute Inc., Cary, NC, USA All rights reserved. Produced in the United States of America. For a hard-copy book: No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the publisher, SAS Institute Inc. For a web download or e-book: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. The scanning, uploading, and distribution of this book via the Internet or any other means without the permission of the publisher is illegal and punishable by law. Please purchase only authorized electronic editions and do not participate in or encourage electronic piracy of copyrighted materials. Your support of others’ rights is appreciated. U.S. Government License Rights; Restricted Rights: The Software and its documentation is commercial computer software developed at private expense and is provided with RESTRICTED RIGHTS to the United States Government. Use, duplication or disclosure of the Software by the United States Government is subject to the license terms of this Agreement pursuant to, as applicable, FAR 12.212, DFAR 227.7202-1(a), DFAR 227.7202-3(a) and DFAR 227.7202-4 and, to the extent required under U.S. -
On Estimating the Reliability in a Multicomponent System Based on Progressively-Censored Data from Chen Distribution
ON ESTIMATING THE RELIABILITY IN A MULTICOMPONENT SYSTEM BASED ON PROGRESSIVELY-CENSORED DATA FROM CHEN DISTRIBUTION By Oluwakorede Daniel Ajumobi Sumith Gunasekera Lakmali Weerasena Associate Professor of Statistics Assistant Professor of Mathematics (Committee Chair) (Committee Member) Ossama Saleh Hong Qin Professor of Mathematics Associate Professor of Computer Science (Committee Member) (Committee Member) ON ESTIMATING THE RELIABILITY IN A MULTICOMPONENT SYSTEM BASED ON PROGRESSIVELY-CENSORED DATA FROM CHEN DISTRIBUTION By Oluwakorede Daniel Ajumobi A Thesis Submitted to the Faculty of the University of Tennessee at Chattanooga in Partial Fulfillment of the Requirements of the Degree of Master of Science: Mathematics The University of Tennessee at Chattanooga, Chattanooga, Tennessee May 2019 ii Copyright c 2019 Oluwakorede Daniel Ajumobi All rights reserved iii ABSTRACT This research deals with classical, Bayesian, and generalized estimation of stress-strength reliability parameter, Rs;k = Pr(at least s of (X1;X2;:::;Xk) exceed Y) = Pr(Xk−s+1:k > Y) of an s-out-of-k : G multicomponent system, based on progressively type-II right-censored samples with random removals when stress and strength are two independent Chen random variables. Under squared-error and LINEX loss functions, Bayes estimates are developed by using Lindley’s approximation and Markov Chain Monte Carlo method. Generalized estimates are developed using generalized variable method while classical estimates - the maximum likelihood estimators, their asymptotic distributions, asymptotic confidence intervals, bootstrap-based confidence intervals - are also developed. A simulation study and a real-world data analysis are provided to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected lengths of the confidence intervals, and biases of the estimators are also computed, compared and contrasted. -
IBM SPSS Exact Tests
IBM SPSS Exact Tests Cyrus R. Mehta and Nitin R. Patel Note: Before using this information and the product it supports, read the general information under Notices on page 213. This edition applies to IBM® SPSS® Exact Tests 22 and to all subsequent releases and modifications until otherwise indicated in new editions. Microsoft product screenshots reproduced with permission from Microsoft Corporation. Licensed Materials - Property of IBM © Copyright IBM Corp. 1989, 2013. U.S. Government Users Restricted Rights - Use, duplication or disclosure restricted by GSA ADP Schedule Contract with IBM Corp. Preface Exact Tests™ is a statistical package for analyzing continuous or categorical data by exact methods. The goal in Exact Tests is to enable you to make reliable inferences when your data are small, sparse, heavily tied, or unbalanced and the validity of the corresponding large sample theory is in doubt. This is achieved by computing exact p values for a very wide class of hypothesis tests, including one-, two-, and K- sample tests, tests for unordered and ordered categorical data, and tests for measures of asso- ciation. The statistical methodology underlying these exact tests is well established in the statistical literature and may be regarded as a natural generalization of Fisher’s ex- act test for the single 22× contingency table. It is fully explained in this user manual. The real challenge has been to make this methodology operational through software development. Historically, this has been a difficult task because the computational de- mands imposed by the exact methods are rather severe. We and our colleagues at the Harvard School of Public Health have worked on these computational problems for over a decade and have developed exact and Monte Carlo algorithms to solve them. -
Sigmaxl Version 7.0 Workbook
SigmaXL® Version 7.0 Workbook Contact Information: Technical Support: 1-866-475-2124 (Toll Free in North America) or 1-519-579-5877 Sales: 1-888-SigmaXL (888-744-6295) E-mail: [email protected] Web: www.SigmaXL.com Copyright © 2004-2014, SigmaXL Inc. Published September, 2014 Table of Contents SigmaXL® Feature List Summary, What’s New in Version 7.0, Installation Notes, System Requirements and Getting Help ............................................................................................ 1 SigmaXL Version 7.0 Feature List Summary ................................................................................... 3 What’s New in Version 7.0 ............................................................................................................. 7 Installation Notes ......................................................................................................................... 11 Activating SigmaXL ................................................................................................................. 15 Error Messages ...................................................................................................................... 18 Installation Notes for Excel 2007/2010/2013 .............................................................................. 19 Installation Notes for Excel Mac 2011 ......................................................................................... 21 SigmaXL® Defaults and Menu Options ........................................................................................