DOCSLIB.ORG

The In-Database Analytics Leader the In-Database Analytics Leader the In-Database Analytics Leader

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The In-Database Analytics Leader the In-Database Analytics Leader the In-Database Analytics Leader The In-Database Analytics Leader The In-Database Analytics Leader The In-Database Analytics Leader Fuzzy Logix DB Lytix™ Advanced Package v1.4.0 Function List on Teradata 14.10/15.00/15.10 94 FLPDFCosine Probability density function of Cosine distribution 145 FLCDFGumbel Cumulative density function of Gumbel distribution 196 FLInvCDFPareto Inverse Cumulative density function of Pareto distribution MATRIX OPERATIONS 247 FLCholeskyDecompUdt Cholesky decomposition 95 FLPDFDoubleGamma Probability density function of DoubleGamma distribution 146 FLCDFHypSecant Cumulative density function of HypSecant distribution 197 FLInvCDFPoisson Inverse Cumulative density function of Poisson distribution 248 FLEigenSystemUdt Eigenvalues & Eigenvectors Generally Available as on Dec 23rd 2015; Total number of functions in package: 547 96 FLPDFDoubleWeibull Probability density function of DoubleWeibull distribution 147 FLCDFInvGamma Cumulative density function of InvGamma distribution 198 FLInvCDFPower Inverse Cumulative density function of Power distribution 249 FLEigenValueUdt Eigenvalues 97 FLPDFErlang Probability density function of Erlang distribution 148 FLCDFInvNormal Cumulative density function of InvNormal distribution 199 FLInvCDFRayleigh Inverse Cumulative density function of Rayleigh distribution 250 FLEigenVectorUdt Eigenvectors Function Category Sr No Function Name Description 47 FLWtAvg Weighted mean 98 FLPDFExp Probability density function of Exp distribution 149 FLCDFLaplace Cumulative density function of Laplace distribution 200 FLInvCDFReciprocal Inverse Cumulative density function of Reciprocal distribution 251 FLHessenbergDecompUdt Hessenberg decomposition BASIC STATS 1 FLCorrel Pearson correlation 48 FLWtCovar Weighted covariance 99 FLPDFExtremeLB Probability density function of ExtremeLB distribution 150 FLCDFLogarithmic Cumulative density function of Logarithmic distribution 201 FLInvCDFSemicircular Inverse Cumulative density function of Semicircular distribution 252 FLJordanDecompUdt Jordan decomposition 2 FLCount Count of observations 49 FLWtStdDev Weighted standard deviation 100 FLPDFFisk Probability density function of Fisk distribution 151 FLCDFLogistic Cumulative density function of Logistic distribution 202 FLInvCDFStudentsT Inverse Cumulative density function of StudentsT distribution 253 FLLUDecompUdt LU decomposition 3 FLCountNeg Count of negative values 50 FLWtVar Weighted variance 101 FLPDFFoldedNormal Probability density function of FoldedNormal distribution 152 FLCDFLogNormal Cumulative density function of LogNormal distribution 203 FLInvCDFTransBeta Inverse Cumulative density function of TransBeta distribution 254 FLMatrixDetUdt Determinant of a matrix 4 FLCountNull Count of null values MATH FNS 51 FLAbs Absolute value 102 FLPDFGamma Probability density function of Gamma distribution 153 FLCDFMaxwell Cumulative density function of Maxwell distribution 204 FLInvCDFTriangular Inverse Cumulative density function of Triangular distribution 255 FLMatrixInvExclUdt Inverse excluding a variable 5 FLCountPos Count of positive values 52 FLBesselI Bessel Function 103 FLPDFGenLogistic Probability density function of GenLogistic distribution 154 FLCDFNegBinomial Cumulative density function of NegBinomial distribution 205 FLInvCDFUniform Inverse Cumulative density function of Uniform distribution 256 FLMatrixInvUdt Inverse of a square matrix 6 FLCountZero Count of zero values 53 FLBesselJ Bessel Function 104 FLPDFGeometric Probability density function of Geometric distribution 155 FLCDFNormal Cumulative density function of Normal distribution 206 FLInvCDFWeibull Inverse Cumulative density function of Weibull distribution 257 FLMatrixNormUdt Norm of a matrix 7 FLCovar Covariance - sample 54 FLBesselK Bessel Function 105 FLPDFGumbel Probability density function of Gumbel distribution 156 FLCDFPareto Cumulative density function of Pareto distribution SIM UNIVARIATE 207 FLSimBeta Simulation of Beta distribution 258 FLMatrixPseudoInvUdt Pseudo inverse of a matrix 8 FLCovarP Covariance - population 55 FLBesselY Bessel Function 106 FLPDFHypSecant Probability density function of HypSecant distribution 157 FLCDFPoisson Cumulative density function of Poisson distribution 208 FLSimBinomial Simulation of Binomial distribution 259 FLMatrixRankUdt Rank of a matrix 9 FLDevSq Sum of squared deviation from mean 56 FLBSplineBasisUdt B-Spline basis factor 107 FLPDFInvGamma Probability density function of InvGamma distribution 158 FLCDFPower Cumulative density function of Power distribution 209 FLSimBradford Simulation of Bradford distribution 260 FLMatrixREFUdt Row echelon form of a matrix 10 FLEuclideanDist Euclidean distance 57 FLCap Cap 108 FLPDFInvNormal Probability density function of InvNormal distribution 159 FLCDFRayleigh Cumulative density function of Rayleigh distribution 210 FLSimBurr Simulation of Burr distribution 261 FLMatrixRREFUdt Reduced row echelon form of a matrix 11 FLFracRank Franctional rank 58 FLCollar Collar 109 FLPDFLaplace Probability density function of Laplace distribution 160 FLCDFReciprocal Cumulative density function of Reciprocal distribution 211 FLSimCauchy Simulation of Cauchy distribution 262 FLMatrixTrace Trace of a matrix or product of two matrices 12 FLGeoMean Geometric mean 59 FLCombin Combination 110 FLPDFLogarithmic Probability density function of Logarithmic distribution 161 FLCDFSemicircular Cumulative density function of Semicircular distribution 212 FLSimChi Simulation of Chi distribution 263 FLPCA Principal component analysis 13 FLHarMean Harmonic mean 60 FLCubicSpline Cubic spline 111 FLPDFLogistic Probability density function of Logistic distribution 162 FLCDFStudentsT Cumulative density function of StudentsT distribution 213 FLSimChiSq Simulation of ChiSq distribution 264 FLQRDecompUdt QR decomposition 14 FLKurtosis Kurtosis 61 FLDeg2Rad Radians from degrees 112 FLPDFLogNormal Probability density function of LogNormal distribution 163 FLCDFTransBeta Cumulative density function of TransBeta distribution 214 FLSimCosine Simulation of Cosine distribution 265 FLSchurDecompUdt Schur decomposition 15 FLMahaDistUdt Mahalanobis distance 62 FLDiGamma Di Gamma function 113 FLPDFMaxwell Probability density function of Maxwell distribution 164 FLCDFTriangular Cumulative density function of Triangular distribution 215 FLSimDoubleGamma Simulation of DoubleGamma distribution 266 FLSVDUdt Singular Value decomposition 16 FLManhattanDist Manhattan distance 63 FLFact Factorial 114 FLPDFNegBinomial Probability density function of NegBinomial distribution 165 FLCDFUniform Cumulative density function of Uniform distribution 216 FLSimDoubleWeibull Simulation of DoubleWeibull distribution 267 FLSVUdt Singular values of a matrix 17 FLMax Maximum 64 FLFloor Floor for input value 115 FLPDFNormal Probability density function of Normal distribution 166 FLCDFWeibull Cumulative density function of Weibull distribution 217 FLSimErlang Simulation of Erlang distribution 268 FLTriDiagUdt Tridiagonalization 18 FLMaxAt The identifier at which the minimum value is reached 65 FLGammaLn Gamma Log 116 FLPDFPareto Probability density function of Pareto distribution INV CDF 167 FLInvCDFBeta Inverse Cumulative density function of Beta distribution 218 FLSimExp Simulation of Exp distribution DATE FUNCTIONS 269 FLDateAdd Add an interval to a date 19 FLMean Arithmetic Mean 66 FLGCD Greatest Common Divisor 117 FLPDFPoisson Probability density function of Poisson distribution 168 FLInvCDFBinomial Inverse Cumulative density function of Binomial distribution 219 FLSimExtremeLB Simulation of ExtremeLB distribution 270 FLDateAddTS Add an interval to a date part of the Timestamp variable 20 FLMeanAbsDevUdt Average absolute deviation from mean 67 FLIncBeta Incomplete beta 118 FLPDFPower Probability density function of Power distribution 169 FLInvCDFBradford Inverse Cumulative density function of Bradford distribution 220 FLSimFisk Simulation of Fisk distribution 271 FLDateConvert Convert a date to a specific format 21 FLMedianAbsDevUdt Average absolute deviation from median 68 FLIncGamma Incomplete gamma 119 FLPDFRayleigh Probability density function of Rayleigh distribution 170 FLInvCDFBurr Inverse Cumulative density function of Burr distribution 221 FLSimFoldedNormal Simulation of FoldedNormal distribution 272 FLDateConvertTS Convert a Timestamp variable to a specific format 22 FLMedianFreq Median based on a histogram 69 FLLCM Least Common Multiple 120 FLPDFReciprocal Probability density function of Reciprocal distribution 171 FLInvCDFCauchy Inverse Cumulative density function of Cauchy distribution 222 FLSimGamma Simulation of Gamma distribution 273 FLDateDiff Compute difference between two dates 23 FLMedianUdt Median 70 FLMod Modulo 121 FLPDFSemicircular Probability density function of Semicircular distribution 172 FLInvCDFChi Inverse Cumulative density function of Chi distribution 223 FLSimGenLogistic Simulation of GenLogistic distribution 274 FLDateDiffTS Compute difference between two Timestamp variables 24 FLMin Minimum 71 FLPermut Permutation 122 FLPDFStudentsT Probability density function of StudentsT distribution 173 FLInvCDFChiSq Inverse Cumulative density function of ChiSq distribution 224 FLSimGeometric Simulation of Geometric distribution 275 FLDatePart Extracts a part of the date variable 25 FLMinAt The identifier at which the maximum value is reached 72 FLRad2Deg Degrees from radians 123 FLPDFTransBeta Probability density function of TransBeta distribution 174 FLInvCDFCosine Inverse Cumulative density function of Cosine
Load more

Recommended publications
  • Methods for Generating Variates From
    METHODS FOR GENERATING VARIATES FROM PROBABILITY DISTRIBUTIONS by JS DAGPUNAR, B. A., M. Sc. A thesis submitted in fulfilment-of the requirements for the award of the degree of Doctor of Philosophy. Department of Mathematics & Statistics, Brunel University, May 1983 (i) JS Dagpunar (1983) Methods for generating variates from probability distributions. Ph. D. Thesig, Department 'of Matbematics, Brunel University ABSTRACT Diverse probabilistic results are used in the design of random univariate generators. General methods based on these are classified and relevant theoretical properiies derived. This is followed by a comparative review of specific algorithms currently available for continuous and discrete univariate distributions. A need for a Zeta generator is established, and two new methods, based on inversion and rejection with a truncated Pareto envelope respectively are developed and compared. The paucity of algorithms for multivariate generation motivates a classification of general methods, and in particular, a new method involving envelope rejection with a novel target distribution is proposed. A new method for generating first passage times in a Wiener Process is constructed. This is based on the ratio of two random numbers, and its performance is compared to an existing method for generating inverse Gaussian variates. New "hybrid" algorithms for Poisson and Negative Binomial distributions are constructed, using an Alias implementation, together with a Geometric tail procedure. These are shown to be robust, exact and fast for a wide range of parameter values. Significant modifications are made to Atkinson's Poisson generator (PA), and the resulting algorithm shown to be complementary to the hybrid method. A new method for Von Mises generation via a comparison of random numbers follows, and its performance compared to that of Best and Fisher's Wrapped Cauchy rejection method.
    [Show full text]
  • Ebookdistributions.Pdf
    DOWNLOAD YOUR FREE MODELRISK TRIAL Adapted from Risk Analysis: a quantitative guide by David Vose. Published by John Wiley and Sons (2008). All Rights Reserved. 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, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. If you notice any errors or omissions, please contact [email protected] Referencing this document Please use the following reference, following the Harvard system of referencing: Van Hauwermeiren M, Vose D and Vanden Bossche S (2012). A Compendium of Distributions (second edition). [ebook]. Vose Software, Ghent, Belgium. Available from www.vosesoftware.com . Accessed dd/mm/yy. © Vose Software BVBA (2012) www.vosesoftware.com Updated 17 January, 2012. Page 2 Table of Contents Introduction .................................................................................................................... 7 DISCRETE AND CONTINUOUS DISTRIBUTIONS.......................................................................... 7 Discrete Distributions .............................................................................................. 7 Continuous Distributions ........................................................................................
    [Show full text]
  • A New Stochastic Asset and Contingent Claim Valuation Framework with Augmented Schrödinger-Sturm-Liouville Eigenprice Conversion
    Coventry University DOCTOR OF PHILOSOPHY A new stochastic asset and contingent claim valuation framework with augmented Schrödinger-Sturm-Liouville EigenPrice conversion Euler, Adrian Award date: 2019 Awarding institution: Coventry University Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of this thesis for personal non-commercial research or study • This thesis cannot be reproduced or quoted extensively from without first obtaining permission from the copyright holder(s) • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 24. Sep. 2021 A New Stochastic Asset and Contingent Claim Valuation Framework with Augmented Schrödinger-Sturm-Liouville Eigen- Price Conversion By Adrian Euler July 10, 2019 A thesis submitted in partial fulfilment of the University’s requirements for the Degree of Doctor of Philosophy EXECUTIVE SUMMARY This study considers a new abstract and probabilistic stochastic finance asset price and contingent claim valuation model with an augmented Schrödinger PDE representation and Sturm-Liouville solutions, leading to additional requirements and outlooks of the probability density function and measurable price quantization effects with increased degrees of freedom.
    [Show full text]
  • Compendium of Common Probability Distributions
    Compendium of Common Probability Distributions Michael P. McLaughlin December, 2016 Compendium of Common Probability Distributions Second Edition, v2.7 Copyright c 2016 by Michael P. McLaughlin. All rights reserved. Second printing, with corrections. DISCLAIMER: This document is intended solely as a synopsis for the convenience of users. It makes no guarantee or warranty of any kind that its contents are appropriate for any purpose. All such decisions are at the discretion of the user. Any brand names and product names included in this work are trademarks, registered trademarks, or trade names of their respective holders. This document created using LATEX and TeXShop. Figures produced using Mathematica. Contents Preface iii Legend v I Continuous: Symmetric1 II Continuous: Skewed 21 III Continuous: Mixtures 77 IV Discrete: Standard 101 V Discrete: Mixtures 115 ii Preface This Compendium is part of the documentation for the software package, Regress+. The latter is a utility intended for univariate mathematical modeling and addresses both deteministic models (equations) as well as stochastic models (distributions). Its focus is on the modeling of empirical data so the models it contains are fully-parametrized variants of commonly used formulas. This document describes the distributions available in Regress+ (v2.7). Most of these are well known but some are not described explicitly in the literature. This Compendium supplies the formulas and parametrization as utilized in the software plus additional formulas, notes, etc. plus one or more
    [Show full text]
  • Probability Distributions
    Probability distributions [Nematrian website page: ProbabilityDistributionsIntro, © Nematrian 2020] The Nematrian website contains information and analytics on a wide range of probability distributions, including: Discrete (univariate) distributions - Bernoulli, see also binomial distribution - Binomial - Geometric, see also negative binomial distribution - Hypergeometric - Logarithmic - Negative binomial - Poisson - Uniform (discrete) Continuous (univariate) distributions - Beta - Beta prime - Burr - Cauchy - Chi-squared - Dagum - Degenerate - Error function - Exponential - F - Fatigue, also known as the Birnbaum-Saunders distribution - Fréchet, see also generalised extreme value (GEV) distribution - Gamma - Generalised extreme value (GEV) - Generalised gamma - Generalised inverse Gaussian - Generalised Pareto (GDP) - Gumbel, see also generalised extreme value (GEV) distribution - Hyperbolic secant - Inverse gamma - Inverse Gaussian - Johnson SU - Kumaraswamy - Laplace - Lévy - Logistic - Log-logistic - Lognormal - Nakagami - Non-central chi-squared - Non-central t - Normal - Pareto - Power function - Rayleigh - Reciprocal - Rice - Student’s t - Triangular - Uniform - Weibull, see also generalised extreme value (GEV) distribution Continuous multivariate distributions - Inverse Wishart Copulas (a copula is a special type of continuous multivariate distribution) - Clayton - Comonotonicity - Countermonotonicity (only valid for 푛 = 2, where 푛 is the dimension of the input) - Frank - Generalised Clayton - Gumbel - Gaussian - Independence
    [Show full text]
  • Estimation for the Mean and the Variance of the Round-Off Error
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Camp. & Marhr. with Apple. Vol. 7. pp 285491. 1981 0097443/81/040285-07SO2.00/0 Printed in Gear Britmn. Pcrgamon Press Ltd. ESTIMATION FOR THE MEAN AND THE VARIANCE OF THE ROUND-OFF ERROR K. OZAWA Department of Information Technology, Sendai Radio Technical College, Kamiayashi Miyagimachi Miyagiken, Japan (Received December 1980) Communicated by Ervin Y. Rodin Abstract-In this paper, the statistical model for the relative round-off error in the floating-point arithmetic is derived. The validity of the model is confirmed by the test of goodness of fit. The formulas to estimate the mean and the variance of the error is also derived. These formulas are applied to the product of the random numbers. Several examples are given which compare the experimental results with the theoretical results. 1. INTRODUCTION We shall consider the round-off error in floating-point arithmetic. In this type of arithmetic, it is convenient to represent the error in relative form, since the bound for the relative error is independent of the input data. We investigate the relative error distribution and derive the formulas to estimate the mean and the variance of the error. 2. RELATIVE ROUND-OFF ERROR Let x be a real number and b 2 2 be an integer, then the normalized base 6 floating-point representation of x is x = (-l)SbEa, (2.1) where s = 0 or 1, i.e. (- 1)” denotes the sign of x, and e and cre[b-‘, l)U{O} are the exponent and the mantissa of x, respectively.
    [Show full text]
  • Engineering Methods in Microsoft Excel
    A SunCam online continuing education course Engineering Methods in Microsoft Excel Part 4: Simulation and Systems Modeling I by Kwabena Ofosu, Ph.D., P.E., PTOE Engineering Methods in Excel A SunCam online continuing education course Abstract This course is part of a series that presents Microsoft Excel tools that are useful for a wide range of engineering analyses and data management. This course covers an introduction to simulation and systems modeling. Simulation is a technique for conducting experimentation of a system or process, virtually, on a computer, using statistical models. This course presents a detailed review of statistical distributions that are widely used in simulation studies. Real-life examples are formulated and implemented in Microsoft Excel and worked using the various Excel tools, spreadsheet techniques, and built-in functions. Examples from various engineering fields are used to demonstrate the concepts and methods learned throughout this course. Upon completion of this course, practitioners will be able to apply the methods learned to a variety of engineering problems, and also to identify situations in their fields of specialty where the innovative application of these tools and methods will be advantageous to their output and to their work product. www.SunCam.com Copyright 2020 Kwabena Ofosu, Ph.D., P.E., PTOE ii Engineering Methods in Excel A SunCam online continuing education course List of Figures Figure 1. 1: Framework for simulation ........................................................................................5
    [Show full text]
  • Driving Etiquette by Huei Peng Professor University of Michigan DISCLAIMER
    Project Start Date: Jan 2018 July 2019 Project End Date: April 2019 Driving Etiquette by Huei Peng Professor University of Michigan DISCLAIMER Funding for this research was provided by the Center for Connected and Automated Transportation under Grant No. 69A3551747105 of the U.S. Department of Transportation, Office of the Assistant Secretary for Research and Technology (OST-R), University Transportation Centers Program. The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the information presented herein. This document is disseminated under the sponsorship of the Department of Transportation, University Transportation Centers Program, in the interest of information exchange. The U.S. Government assumes no liability for the contents or use thereof. Suggested APA Format Citation: Peng, H. & Huang, X. (2019). Driving Etiquette. Final Report. USDOT CCAT Project No. 1 Identifier: http://hdl.handle.net/2027.42/156052 For more information: Huei Peng CCAT 2905 Baxter Road University of Michigan Transportation Research Institute Ann Arbor, MI 48109 2901 Baxter Road [email protected] Ann Arbor, MI 48109 (734) 764-6505 [email protected] (734) 763-2498 Technical Report Documentation Page 1. Report No. 2. Government Accession No. 3. Recipient’s Catalog No. Leave blank – not used Leave blank - not used 4. Title and Subtitle 5. Report Date Driving Etiquette July 2019 Identifier:http://hdl.handle.net/2027.42/156052 6. Performing Organization Code Enter any/all unique numbers assigned to the performing organization, if applicable. 7. Author(s) 8. Performing Organization Report No. Huei Peng, Ph.D. https://orcid.org/0000-0002-7684-1696 Enter any/all unique alphanumeric report Xianan Huang.
    [Show full text]
  • Why Some Families of Probability Distributions Are Practically Efficient
    Why Some Families of Probability Distributions Are Practically Efficient: A Symmetry-Based Explanation Vladik Kreinovich, Olga Kosheleva, Hung T. Nguyen, and Songsak Sriboonchitta Abstract Out of many possible families of probability distributions, some families turned out to be most efficient in practical situations. Why these particular families and not others? To explain this empirical success, we formulate the general problem of selecting a distribution with the largest possible utility under appropriate con- straints. We then show that if we select the utility functional and the constraints which are invariant under natural symmetries – shift and scaling corresponding to changing the starting point and the measuring unit for describing the corresponding quantity x. then the resulting optimal families of probability distributions indeed in- clude most of the empirically successful families. Thus, we get a symmetry-based explanation for their empirical success. Vladik Kreinovich Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, Texas 79968, USA, e-mail: [email protected] Olga Kosheleva University of Texas at El Paso, 500 W. University, El Paso, TX 79968, USA, e-mail: [email protected] Hung T. Nguyen Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mex- ico 88003, USA, and Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand, e-mail: [email protected] Songsak Sriboonchitta Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand, e-mail: [email protected] 1 2 V. Kreinovich, O. Kosheleva, H. T. Nguyen, and S. Sriboonchitta 1 Formulation of the Problem Some families of probability distributions are empirically successful.
    [Show full text]
  • Probability Distribution Compendium
    RReeggrreessss++ Appendix A A Compendium of Common Probability Distributions Version 2.3 © Dr. Michael P. McLaughlin 1993-2001 Third printing This software and its documentation are distributed free of charge and may neither be sold nor repackaged for sale in whole or in part. A-2 PREFACE This Appendix contains summaries of the probability distributions found in Regress+. All distributions are shown in their parameterized, not standard forms. In some cases, the definition of a distribution may vary slightly from a definition given in the literature. This happens either because there is more than one definition or, in the case of parameters, because Regress+ requires a parameter to be constrained, usually to guarantee convergence. There are a few well-known distributions that are not included here, either because they are seldom used to model empirical data or they lack a convenient analytical form for the CDF. Conversely, many of the distributions that are included are rarely discussed yet are very useful for describing real-world datasets. Please email any comments to the author: [email protected] Michael P. McLaughlin McLean, VA September, 1999 A-3 A-4 Table of Contents Distributions shown in bold are those which appear in the Regress+ menu. Distributions shown in plain text are aliases and/or special cases. Continuous Distributions Name Page Name Page Antilognormal 77 HalfNormal(A,B) 51 Bell curve 85 HyperbolicSecant(A,B) 59 Beta(A,B,C,D) 9 Inverse Gaussian 61 Bilateral exponential 63 InverseNormal(A,B) 61 Bradford(A,B,C) 15 Laplace(A,B)
    [Show full text]
  • Sub-Independence: an Expository Perspective
    Marquette University e-Publications@Marquette Mathematics, Statistics and Computer Science Mathematics, Statistics and Computer Science, Faculty Research and Publications Department of (- 2019) 9-2013 Sub-Independence: An Expository Perspective Gholamhossein Hamedani Marquette University, [email protected] Follow this and additional works at: https://epublications.marquette.edu/mscs_fac Part of the Computer Sciences Commons, Mathematics Commons, and the Statistics and Probability Commons Recommended Citation Hamedani, Gholamhossein, "Sub-Independence: An Expository Perspective" (2013). Mathematics, Statistics and Computer Science Faculty Research and Publications. 165. https://epublications.marquette.edu/mscs_fac/165 Marquette University e-Publications@Marquette Mathematics and Statistical Sciences Faculty Research and Publications/College of Arts and Sciences This paper is NOT THE PUBLISHED VERSION; but the author’s final, peer-reviewed manuscript. The published version may be accessed by following the link in the citation below. Communications in Statistics : Theory and Methods, Vol. 42, No. 20 (2013): 3615-3638. DOI. This article is © Taylor & Francis and permission has been granted for this version to appear in e- Publications@Marquette. Taylor & Francis does not grant permission for this article to be further copied/distributed or hosted elsewhere without the express permission from Taylor & Francis. Sub-Independence: An Expository Perspective G. G. Hamedani Department of Mathematics, Statistics and Computer Sciences, Marquette University, Milwaukee, WI Abstract Limit theorems as well as other well-known results in probability and statistics are often based on the distribution of the sums of independent random variables. The concept of sub-independence, which is much weaker than that of independence, is shown to be sufficient to yield the conclusions of these theorems and results.
    [Show full text]
  • Contributions to Statistical Distribution Theory with Applications
    CONTRIBUTIONS TO STATISTICAL DISTRIBUTION THEORY WITH APPLICATIONS A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Science and Engineering 2018 By Xiao Jiang School of Mathematics Contents Abstract 10 Declaration 11 Copyright 12 Acknowledgements 13 1 Introduction 14 1.1 Aims . 14 1.2 Motivations and contributions . 15 2 Generalized hyperbolic distributions 17 2.1 Introduction . 17 2.2 The collection . 18 2.2.1 Generalized hyperbolic distribution . 19 2.2.2 Hyperbolic distribution . 20 2.2.3 Log hyperbolic distribution . 20 2.2.4 Normal inverse Gaussian distribution . 21 2.2.5 Variance gamma distribution . 21 2.2.6 Generalized inverse Gaussian distribution . 22 2 2.2.7 Student's t distribution . 23 2.2.8 Normal distribution . 23 2.2.9 GH skew Student's t distribution . 23 2.2.10 Mixture of GH distributions . 24 2.2.11 Geometric GH distribution . 24 2.2.12 Generalized generalized inverse Gaussian distribution . 24 2.2.13 Logarithmic generalized inverse Gaussian distribution . 25 2.2.14 Ψ2 hypergeometric generalized inverse Gaussian distribution . 25 2.2.15 Confluent hypergeometric generalized inverse Gaussian distribution . 26 2.2.16 Nakagami generalized inverse Gaussian distribution . 27 2.2.17 Generalized Nakagami generalized inverse Gaussian distribution . 28 2.2.18 Extended generalized inverse Gaussian distribution . 28 2.2.19 Exponential reciprocal generalized inverse Gaussian distribution . 29 2.2.20 Gamma generalized inverse Gaussian distribution . 29 2.2.21 Exponentiated generalized inverse Gaussian distribution . 30 2.3 Real data application . 31 2.4 Computer software . 32 3 Smallest Pareto order statistics 37 3.1 Introduction .
    [Show full text]