Measures of Central Tendency
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Comparison of Harmonic, Geometric and Arithmetic Means for Change Detection in SAR Time Series Guillaume Quin, Béatrice Pinel-Puysségur, Jean-Marie Nicolas
Comparison of Harmonic, Geometric and Arithmetic means for change detection in SAR time series Guillaume Quin, Béatrice Pinel-Puysségur, Jean-Marie Nicolas To cite this version: Guillaume Quin, Béatrice Pinel-Puysségur, Jean-Marie Nicolas. Comparison of Harmonic, Geometric and Arithmetic means for change detection in SAR time series. EUSAR. 9th European Conference on Synthetic Aperture Radar, 2012., Apr 2012, Germany. hal-00737524 HAL Id: hal-00737524 https://hal.archives-ouvertes.fr/hal-00737524 Submitted on 2 Oct 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. EUSAR 2012 Comparison of Harmonic, Geometric and Arithmetic Means for Change Detection in SAR Time Series Guillaume Quin CEA, DAM, DIF, F-91297 Arpajon, France Béatrice Pinel-Puysségur CEA, DAM, DIF, F-91297 Arpajon, France Jean-Marie Nicolas Telecom ParisTech, CNRS LTCI, 75634 Paris Cedex 13, France Abstract The amplitude distribution in a SAR image can present a heavy tail. Indeed, very high–valued outliers can be observed. In this paper, we propose the usage of the Harmonic, Geometric and Arithmetic temporal means for amplitude statistical studies along time. In general, the arithmetic mean is used to compute the mean amplitude of time series. -
University of Cincinnati
UNIVERSITY OF CINCINNATI Date:___________________ I, _________________________________________________________, hereby submit this work as part of the requirements for the degree of: in: It is entitled: This work and its defense approved by: Chair: _______________________________ _______________________________ _______________________________ _______________________________ _______________________________ Gibbs Sampling and Expectation Maximization Methods for Estimation of Censored Values from Correlated Multivariate Distributions A dissertation submitted to the Division of Research and Advanced Studies of the University of Cincinnati in partial ful…llment of the requirements for the degree of DOCTORATE OF PHILOSOPHY (Ph.D.) in the Department of Mathematical Sciences of the McMicken College of Arts and Sciences May 2008 by Tina D. Hunter B.S. Industrial and Systems Engineering The Ohio State University, Columbus, Ohio, 1984 M.S. Aerospace Engineering University of Cincinnati, Cincinnati, Ohio, 1989 M.S. Statistics University of Cincinnati, Cincinnati, Ohio, 2003 Committee Chair: Dr. Siva Sivaganesan Abstract Statisticians are often called upon to analyze censored data. Environmental and toxicological data is often left-censored due to reporting practices for mea- surements that are below a statistically de…ned detection limit. Although there is an abundance of literature on univariate methods for analyzing this type of data, a great need still exists for multivariate methods that take into account possible correlation amongst variables. Two methods are developed here for that purpose. One is a Markov Chain Monte Carlo method that uses a Gibbs sampler to es- timate censored data values as well as distributional and regression parameters. The second is an expectation maximization (EM) algorithm that solves for the distributional parameters that maximize the complete likelihood function in the presence of censored data. -
Simple Mean Weighted Mean Or Harmonic Mean
MultiplyMultiply oror Divide?Divide? AA BestBest PracticePractice forfor FactorFactor AnalysisAnalysis 77 ––10 10 JuneJune 20112011 Dr.Dr. ShuShu-Ping-Ping HuHu AlfredAlfred SmithSmith CCEACCEA Los Angeles Washington, D.C. Boston Chantilly Huntsville Dayton Santa Barbara Albuquerque Colorado Springs Ft. Meade Ft. Monmouth Goddard Space Flight Center Ogden Patuxent River Silver Spring Washington Navy Yard Cleveland Dahlgren Denver Johnson Space Center Montgomery New Orleans Oklahoma City Tampa Tacoma Vandenberg AFB Warner Robins ALC Presented at the 2011 ISPA/SCEA Joint Annual Conference and Training Workshop - www.iceaaonline.com PRT-70, 01 Apr 2011 ObjectivesObjectives It is common to estimate hours as a simple factor of a technical parameter such as weight, aperture, power or source lines of code (SLOC), i.e., hours = a*TechParameter z “Software development hours = a * SLOC” is used as an example z Concept is applicable to any factor cost estimating relationship (CER) Our objective is to address how to best estimate “a” z Multiply SLOC by Hour/SLOC or Divide SLOC by SLOC/Hour? z Simple, weighted, or harmonic mean? z Role of regression analysis z Base uncertainty on the prediction interval rather than just the range Our goal is to provide analysts a better understanding of choices available and how to select the right approach Presented at the 2011 ISPA/SCEA Joint Annual Conference and Training Workshop - www.iceaaonline.com PR-70, 01 Apr 2011 Approved for Public Release 2 of 25 OutlineOutline Definitions -
Incorporating a Geometric Mean Formula Into The
Calculating the CPI Incorporating a geometric mean formula into the CPI Beginning in January 1999, a new geometric mean formula will replace the current Laspeyres formula in calculating most basic components of the Consumer Price Index; the new formula will better account for the economic substitution behavior of consumers 2 Kenneth V. Dalton, his article describes an important improve- bias” in the CPI. This upward bias was a techni- John S. Greenlees, ment in the calculation of the Consumer cal problem that tied the weight of a CPI sample and TPrice Index (CPI). The Bureau of Labor Sta- item to its expected price change. The flaw was Kenneth J. Stewart tistics plans to use a new geometric mean for- effectively eliminated by changes to the CPI mula for calculating most of the basic compo- sample rotation and substitution procedures and nents of the Consumer Price Index for all Urban to the functional form used to calculate changes Consumers (CPI-U) and the Consumer Price In- in the cost of shelter for homeowners. In 1997, a dex for Urban Wage Earners and Clerical Work- new approach to the measurement of consumer ers (CPI-W). This change will become effective prices for hospital services was introduced.3 Pric- with data for January 1999.1 ing procedures were revised, from pricing indi- The geometric mean formula will be used in vidual items (such as a unit of blood or a hospi- index categories that make up approximately 61 tal inpatient day) to pricing the combined sets of percent of total consumer spending represented goods and services provided on selected patient by the CPI-U. -
Wavelet Operators and Multiplicative Observation Models
Wavelet Operators and Multiplicative Observation Models - Application to Change-Enhanced Regularization of SAR Image Time Series Abdourrahmane Atto, Emmanuel Trouvé, Jean-Marie Nicolas, Thu Trang Le To cite this version: Abdourrahmane Atto, Emmanuel Trouvé, Jean-Marie Nicolas, Thu Trang Le. Wavelet Operators and Multiplicative Observation Models - Application to Change-Enhanced Regularization of SAR Image Time Series. 2016. hal-00950823v3 HAL Id: hal-00950823 https://hal.archives-ouvertes.fr/hal-00950823v3 Preprint submitted on 26 Jan 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. 1 Wavelet Operators and Multiplicative Observation Models - Application to Change-Enhanced Regularization of SAR Image Time Series Abdourrahmane M. Atto1;∗, Emmanuel Trouve1, Jean-Marie Nicolas2, Thu-Trang Le^1 Abstract|This paper first provides statistical prop- I. Introduction - Motivation erties of wavelet operators when the observation model IGHLY resolved data such as Synthetic Aperture can be seen as the product of a deterministic piece- Radar (SAR) image time series issued from new wise regular function (signal) and a stationary random H field (noise). This multiplicative observation model is generation sensors show minute details. Indeed, the evo- analyzed in two standard frameworks by considering lution of SAR imaging systems is such that in less than 2 either (1) a direct wavelet transform of the model decades: or (2) a log-transform of the model prior to wavelet • high resolution sensors can achieve metric resolution, decomposition. -
“Mean”? a Review of Interpreting and Calculating Different Types of Means and Standard Deviations
pharmaceutics Review What Does It “Mean”? A Review of Interpreting and Calculating Different Types of Means and Standard Deviations Marilyn N. Martinez 1,* and Mary J. Bartholomew 2 1 Office of New Animal Drug Evaluation, Center for Veterinary Medicine, US FDA, Rockville, MD 20855, USA 2 Office of Surveillance and Compliance, Center for Veterinary Medicine, US FDA, Rockville, MD 20855, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-240-3-402-0635 Academic Editors: Arlene McDowell and Neal Davies Received: 17 January 2017; Accepted: 5 April 2017; Published: 13 April 2017 Abstract: Typically, investigations are conducted with the goal of generating inferences about a population (humans or animal). Since it is not feasible to evaluate the entire population, the study is conducted using a randomly selected subset of that population. With the goal of using the results generated from that sample to provide inferences about the true population, it is important to consider the properties of the population distribution and how well they are represented by the sample (the subset of values). Consistent with that study objective, it is necessary to identify and use the most appropriate set of summary statistics to describe the study results. Inherent in that choice is the need to identify the specific question being asked and the assumptions associated with the data analysis. The estimate of a “mean” value is an example of a summary statistic that is sometimes reported without adequate consideration as to its implications or the underlying assumptions associated with the data being evaluated. When ignoring these critical considerations, the method of calculating the variance may be inconsistent with the type of mean being reported. -
Harmonic Means Mean of a Ratio Summarizing Variability: Range, Variance, Percentiles, Quartiles Determining Distribution of Data: Quantile-Quantile Plots
SummarizingSummarizing MeasuredMeasured DataData ©2010 Raj Jain www.rajjain.com 12-1 OverviewOverview Basic Probability and Statistics Concepts: CDF, PDF, PMF, Mean, Variance, CoV, Normal Distribution Summarizing Data by a Single Number: Mean, Median, and Mode, Arithmetic, Geometric, Harmonic Means Mean of A Ratio Summarizing Variability: Range, Variance, percentiles, Quartiles Determining Distribution of Data: Quantile-Quantile plots ©2010 Raj Jain www.rajjain.com 12-2 PartPart III:III: ProbabilityProbability TheoryTheory andand StatisticsStatistics 1. How to report the performance as a single number? Is specifying the mean the correct way? 2. How to report the variability of measured quantities? What are the alternatives to variance and when are they appropriate? 3. How to interpret the variability? How much confidence can you put on data with a large variability? 4. How many measurements are required to get a desired level of statistical confidence? 5. How to summarize the results of several different workloads on a single computer system? 6. How to compare two or more computer systems using several different workloads? Is comparing the mean sufficient? 7. What model best describes the relationship between two variables? Also, how good is the model? ©2010 Raj Jain www.rajjain.com 12-3 BasicBasic ProbabilityProbability andand StatisticsStatistics ConceptsConcepts Independent Events: Two events are called independent if the occurrence of one event does not in any way affect the probability of the other event. Random Variable: -
Expectation and Functions of Random Variables
POL 571: Expectation and Functions of Random Variables Kosuke Imai Department of Politics, Princeton University March 10, 2006 1 Expectation and Independence To gain further insights about the behavior of random variables, we first consider their expectation, which is also called mean value or expected value. The definition of expectation follows our intuition. Definition 1 Let X be a random variable and g be any function. 1. If X is discrete, then the expectation of g(X) is defined as, then X E[g(X)] = g(x)f(x), x∈X where f is the probability mass function of X and X is the support of X. 2. If X is continuous, then the expectation of g(X) is defined as, Z ∞ E[g(X)] = g(x)f(x) dx, −∞ where f is the probability density function of X. If E(X) = −∞ or E(X) = ∞ (i.e., E(|X|) = ∞), then we say the expectation E(X) does not exist. One sometimes write EX to emphasize that the expectation is taken with respect to a particular random variable X. For a continuous random variable, the expectation is sometimes written as, Z x E[g(X)] = g(x) d F (x). −∞ where F (x) is the distribution function of X. The expectation operator has inherits its properties from those of summation and integral. In particular, the following theorem shows that expectation preserves the inequality and is a linear operator. Theorem 1 (Expectation) Let X and Y be random variables with finite expectations. 1. If g(x) ≥ h(x) for all x ∈ R, then E[g(X)] ≥ E[h(X)]. -
Notes on Calculating Computer Performance
Notes on Calculating Computer Performance Bruce Jacob and Trevor Mudge Advanced Computer Architecture Lab EECS Department, University of Michigan {blj,tnm}@umich.edu Abstract This report explains what it means to characterize the performance of a computer, and which methods are appro- priate and inappropriate for the task. The most widely used metric is the performance on the SPEC benchmark suite of programs; currently, the results of running the SPEC benchmark suite are compiled into a single number using the geometric mean. The primary reason for using the geometric mean is that it preserves values across normalization, but unfortunately, it does not preserve total run time, which is probably the figure of greatest interest when performances are being compared. Cycles per Instruction (CPI) is another widely used metric, but this method is invalid, even if comparing machines with identical clock speeds. Comparing CPI values to judge performance falls prey to the same prob- lems as averaging normalized values. In general, normalized values must not be averaged and instead of the geometric mean, either the harmonic or the arithmetic mean is the appropriate method for averaging a set running times. The arithmetic mean should be used to average times, and the harmonic mean should be used to average rates (1/time). A number of published SPECmarks are recomputed using these means to demonstrate the effect of choosing a favorable algorithm. 1.0 Performance and the Use of Means We want to summarize the performance of a computer; the easiest way uses a single number that can be compared against the numbers of other machines. -
Package 'Cumstats'
Package ‘cumstats’ January 16, 2017 Type Package Title Cumulative Descriptive Statistics Version 1.0 Date 2017-01-13 Author Arturo Erdely and Ian Castillo Maintainer Arturo Erdely <[email protected]> Description Cumulative descriptive statistics for (arithmetic, geometric, harmonic) mean, me- dian, mode, variance, skewness and kurtosis. License GPL-3 NeedsCompilation no Repository CRAN Date/Publication 2017-01-16 08:13:00 R topics documented: cumstats-package . .2 cumgmean . .3 cumhmean . .4 cumkurt . .5 cummean . .6 cummedian . .7 cummode . .8 cumquant . .9 cumskew . 10 cumvar . 11 kurtosis . 11 Mode ............................................ 12 skewness . 13 Index 15 1 2 cumstats-package cumstats-package Cumulative Descriptive Statistics Description Cumulative descriptive statistics for (arithmetic, geometric, harmonic) mean, median, mode, vari- ance, skewness and kurtosis. Details The DESCRIPTION file: Package: cumstats Type: Package Title: Cumulative Descriptive Statistics Version: 1.0 Date: 2017-01-13 Author: Arturo Erdely and Ian Castillo Maintainer: Arturo Erdely <[email protected]> Description: Cumulative descriptive statistics for (arithmetic, geometric, harmonic) mean, median, mode, variance, skewness and kurtosis. License: GPL-3 Index of help topics: Mode Statistical Mode cumgmean Cumulative Geometric Mean cumhmean Cumulative Harmonic Mean cumkurt Cumulative Kurtosis cummean Cumulative Arithmetic Mean cummedian Cumulative Median cummode Cumulative Mode cumquant Cumulative Quantile cumskew Cumulative Skewness cumstats-package Cumulative Descriptive Statistics cumvar Cumulative Variance kurtosis Pearson's Measure of Kurtosis skewness Skewness Cumulative descriptive statistics for (arithmetic, geometric, harmonic) mean, median, mode, vari- ance, skewness and kurtosis. Author(s) Arturo Erdely and Ian Castillo Maintainer: Arturo Erdely <[email protected]> cumgmean 3 cumgmean Cumulative Geometric Mean Description Returns a vector whose elements are the cumulative geometric mean of the elements of the argu- ment. -
[Math.PR] 3 Dec 2001 Nsm Eali Eto .;Hr Ewl Utrcl H Essentials
HARMONIC MEAN, RANDOM POLYNOMIALS AND STOCHASTIC MATRICES NATALIA L. KOMAROVA AND IGOR RIVIN Abstract. Motivated by a problem in learning theory, we are led to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the derivative of random polynomials (generated by picking their roots uniformly at random in the interval [0, 1], although our results extend to other distribu- tions). This, in turn, requires the study of the statistical behavior of the harmonic mean of random variables as above, and that, in turn, leads us to delicate question of the rate of convergence to stable laws and tail estimates for stable laws. Introduction The original motivation for the work in this paper was provided by the first-named author’s research in learning theory, specifically in various models of language acquisition (see [KNN2001, NKN2001, KN2001]) and more specifically yet by the analysis of the speed of con- vergence of the memoryless learner algorithm. The setup is described in some detail in Section 4.1; here we will just recall the essentials. There is a collection of concepts R1,...,Rn and words which refer to these concepts, sometimes ambiguously. The teacher generates a stream of words, referring to the concept R1. This is not known to the student, but he must learn by, at each steps, guessing some concept Ri and checking for consistency with the teacher’s input. The mem- oryless learner algorithm consists of picking a concept Ri at random, arXiv:math/0105236v2 [math.PR] 3 Dec 2001 and sticking by this choice, until it is proven wrong. -
E5df876f5e0f28178c70af790e47
Journal of Applied Pharmaceutical Science Vol. 8(07), pp 001-009, July, 2018 Available online at http://www.japsonline.com DOI: 10.7324/JAPS.2018.8701 ISSN 2231-3354 Application of Chemometrics for the simultaneous estimation of stigmasterol and β-sitosterol in Manasamitra Vatakam-an ayurvedic herbomineral formulation using HPLC-PDA method Srikalyani Vemuri1, Mohan Kumar Ramasamy1, Pandiyan Rajakanu1, Rajappan Chandra Satish Kumar2, Ilango Kalliappan1,3* 1Division of Analytical Chemistry, Interdisciplinary Institute of Indian System of Medicine (IIISM), SRM Institute of Science and Technology, Kattanku- lathur-603 203, Kancheepuram (Dt), Tamil Nadu, India. 2Clinical Trial and Research Unit (Metabolic Ward), Interdisciplinary Institute of Indian System of Medicine (IIISM), SRM Institute of Science and Tech- nology, Kattankulathur-603 203, Kancheepuram (Dt), Tamil Nadu, India. 3Department of Pharmaceutical Chemistry, SRM College of Pharmacy, SRM Institute of Science and Technology, Kattankulathur-603 203, Kancheepuram (Dt), Tamil Nadu, India. ARTICLE INFO ABSTRACT Article history: A new research method has been developed to approach multiresponse optimization for simultaneously optimizing Received on: 08/05/2018 a large number of experimental factors. LC Chromatogram was optimized using Phenomenex RP C18 column (250 x Accepted on: 15/06/2018 4.6 mm; 5 µm); mobile phase was surged at isocratic mode with a flow of 1.0 mL/min using methanol and acetonitrile Available online: 30/07/2018 (95:5% v/v) at the detection max of 208 nm with the retention time of 16.3 and 18.1 min for Stigmasterol and β-Sitosterol respectively. Amount of Stigmasterol and β-Sitosterol was quantified and found to be 51.0 and 56.3 µg/ mg respectively.