Statistics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=167
en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 25 Apr 2014 02:44:03 GMTFri, 25 Apr 2014 02:44:03 GMTNew applications in the Statistics categoryhttp://www.mapleprimes.com/images/mapleapps.gifStatistics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=167
Wavelet analysis of the blood pressure and pulse frequency measurements with Maple
http://www.maplesoft.com/applications/view.aspx?SID=149420&ref=Feed
<p>A significant part of medical signals, or observations, is non-stationary, discrete time sequences. Thus, the computer methods analysis, as well as refinement and compression, are very helpful as for the problems of recognition and detection of their key diagnostic features. We are going to illustrate here this statement with examples of very common, and even routine medical measurements of blood pressure as well as pulse rate and with possibilities of Maple.<br />The package of Discrete Wavelet transforms (DWT) within Maple 16 [1] was recently added as new research software just for such tasks. The practical testing of this package was additional goal of present study.</p><img src="/view.aspx?si=149420/4b9024ee653d2c7be8febb717b1df52a.gif" alt="Wavelet analysis of the blood pressure and pulse frequency measurements with Maple" align="left"/><p>A significant part of medical signals, or observations, is non-stationary, discrete time sequences. Thus, the computer methods analysis, as well as refinement and compression, are very helpful as for the problems of recognition and detection of their key diagnostic features. We are going to illustrate here this statement with examples of very common, and even routine medical measurements of blood pressure as well as pulse rate and with possibilities of Maple.<br />The package of Discrete Wavelet transforms (DWT) within Maple 16 [1] was recently added as new research software just for such tasks. The practical testing of this package was additional goal of present study.</p>149420Sun, 14 Jul 2013 04:00:00 ZIrina A. DanishewskaIrina A. DanishewskaClassroom Tips and Techniques: Least-Squares Fits
http://www.maplesoft.com/applications/view.aspx?SID=140942&ref=Feed
<p><span id="ctl00_mainContent__documentViewer" ><span ><span class="body summary">The least-squares fitting of functions to data can be done in Maple with eleven different commands from four different packages. The <em>CurveFitting</em> and LinearAlgebra packages each have a LeastSquares command; the Optimization package has the LSSolve and NLPSolve commands; and the Statistics package has the seven commands Fit, LinearFit, PolynomialFit, ExponentialFit, LogarithmicFit, PowerFit, and NonlinearFit, which can return some measure of regression analysis.</span></span></span></p><img src="/view.aspx?si=140942/image.jpg" alt="Classroom Tips and Techniques: Least-Squares Fits" align="left"/><p><span id="ctl00_mainContent__documentViewer" ><span ><span class="body summary">The least-squares fitting of functions to data can be done in Maple with eleven different commands from four different packages. The <em>CurveFitting</em> and LinearAlgebra packages each have a LeastSquares command; the Optimization package has the LSSolve and NLPSolve commands; and the Statistics package has the seven commands Fit, LinearFit, PolynomialFit, ExponentialFit, LogarithmicFit, PowerFit, and NonlinearFit, which can return some measure of regression analysis.</span></span></span></p>140942Wed, 28 Nov 2012 05:00:00 ZDr. Robert LopezDr. Robert LopezStatistics Enhancements in Maple 16
http://www.maplesoft.com/applications/view.aspx?SID=132195&ref=Feed
Statistical computations in Maple combine the ease of working in a high-level, interactive environment with a very large and powerful set of algorithms. Large data sets can be handled efficiently with 35 built-in statistical distributions, sampling, estimations, data smoothing, hypothesis testing, and visualization algorithms. In addition, integration with the Maple symbolic engine means that you can easily specify custom distributions by combining existing distributions or simply by giving a formula for the probability or cumulative distribution function. These examples illustrate the use of the Statistics package, with emphasis on enhancements in Maple 16.<img src="/view.aspx?si=132195/thumb.jpg" alt="Statistics Enhancements in Maple 16" align="left"/>Statistical computations in Maple combine the ease of working in a high-level, interactive environment with a very large and powerful set of algorithms. Large data sets can be handled efficiently with 35 built-in statistical distributions, sampling, estimations, data smoothing, hypothesis testing, and visualization algorithms. In addition, integration with the Maple symbolic engine means that you can easily specify custom distributions by combining existing distributions or simply by giving a formula for the probability or cumulative distribution function. These examples illustrate the use of the Statistics package, with emphasis on enhancements in Maple 16.132195Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftClassroom Tips and Techniques: Gems 21-25 from the Red Book of Maple Magic
http://www.maplesoft.com/applications/view.aspx?SID=127613&ref=Feed
From the Red Book of Maple Magic, Gems 21-25: Simplifying an absolute value, extracting coefficients from a complete quadratic, "dot and stick" graphs of discrete data, restoring the order of terms in an expression, and finding the smallest positive zero of a non-polynomial function.<img src="/view.aspx?si=127613/thumb2.jpg" alt="Classroom Tips and Techniques: Gems 21-25 from the Red Book of Maple Magic" align="left"/>From the Red Book of Maple Magic, Gems 21-25: Simplifying an absolute value, extracting coefficients from a complete quadratic, "dot and stick" graphs of discrete data, restoring the order of terms in an expression, and finding the smallest positive zero of a non-polynomial function.127613Wed, 09 Nov 2011 05:00:00 ZDr. Robert LopezDr. Robert LopezGreat Expectations
http://www.maplesoft.com/applications/view.aspx?SID=127116&ref=Feed
<p>An investor is offered what appears to be a great investment opportunity. Unfortunately it doesn't turn out to be so great in the long run. This interactive Maple document explores the situation using simulation and analysis, and suggests a new strategy that would produce better results.</p>
<p>This is an example suitable for presentation in an undergraduate course on probability. No knowledge of Maple is required.</p><img src="/view.aspx?si=127116/expectation_thum.png" alt="Great Expectations" align="left"/><p>An investor is offered what appears to be a great investment opportunity. Unfortunately it doesn't turn out to be so great in the long run. This interactive Maple document explores the situation using simulation and analysis, and suggests a new strategy that would produce better results.</p>
<p>This is an example suitable for presentation in an undergraduate course on probability. No knowledge of Maple is required.</p>127116Thu, 27 Oct 2011 04:00:00 ZThe Advanced Encryption Standard and its modes of operation
http://www.maplesoft.com/applications/view.aspx?SID=6618&ref=Feed
<p>This is an update, labeled version 1.1, to the existing application The Advanced Encryption Standard and its modes of operation.</p>
<p>Version 1.1: Key generation function and related functions updated to facilitate the use of externally generated seeds. Some minor changes to presentation.</p>
<p>Version 1.0: Implementation of encryption and authentication schemes that use the Advanced Encryption Standard (AES) as their underlying block cipher. These schemes are constructed by using all the modes of operation for block ciphers so far approved by NIST (the US National Institute of Standards of Technology), namely, the five confidentiality modes: ECB, CBC, CFB, OFB and CTR, the authentication mode CMAC, and the "authenticated encryption" modes CCM and GCM/GMAC. The implementation is able to encrypt/decrypt and/or authenticate messages in several formats, including binary files, and we use it to explore the basic properties of these schemes. The implementation contains also detailed explanations of all the procedures used, including the lower level ones, and discusses both the programming and the cryptographic aspects involved.</p><img src="/view.aspx?si=6618/AES_1608.gif" alt="The Advanced Encryption Standard and its modes of operation" align="left"/><p>This is an update, labeled version 1.1, to the existing application The Advanced Encryption Standard and its modes of operation.</p>
<p>Version 1.1: Key generation function and related functions updated to facilitate the use of externally generated seeds. Some minor changes to presentation.</p>
<p>Version 1.0: Implementation of encryption and authentication schemes that use the Advanced Encryption Standard (AES) as their underlying block cipher. These schemes are constructed by using all the modes of operation for block ciphers so far approved by NIST (the US National Institute of Standards of Technology), namely, the five confidentiality modes: ECB, CBC, CFB, OFB and CTR, the authentication mode CMAC, and the "authenticated encryption" modes CCM and GCM/GMAC. The implementation is able to encrypt/decrypt and/or authenticate messages in several formats, including binary files, and we use it to explore the basic properties of these schemes. The implementation contains also detailed explanations of all the procedures used, including the lower level ones, and discusses both the programming and the cryptographic aspects involved.</p>6618Mon, 20 Jun 2011 04:00:00 ZJosé Luis Gómez PardoJosé Luis Gómez PardoExotic EIE-course
http://www.maplesoft.com/applications/view.aspx?SID=102076&ref=Feed
<p>Ukraine. <br />Exotic training course for the entrance examination in mathematics.<br /><strong>External independent evaluation</strong> <br />Themes:<br />0101 Goals and rational number <br />0102 Interest. The main problem of interest <br />0103 The simplest geometric shapes on the plane and their properties <br />0201 Degree of natural and integral indicator <br />0202 Monomial and polynomials and operations on them <br />0203 Triangles and their basic properties <br />0301 Algebraic fractions and operations on them <br />0302 Square root. Real numbers <br />0303 Circle and circle, their properties <br />0401 Equations, inequalities and their systems <br />0402 Function and its basic properties <br />0403 Described and inscribed triangles <br />0501 Linear function, linear equations, inequalities and their systems <br />0502 Quadratic function, quadratic equation, inequality and their systems <br />0503 Solving square triangles <br />0601 Rational Equations, Inequalities and their sysytemy <br />0602 Numerical sequence. Arithmetic and geometric progression <br />0603 Solving arbitrary triangles <br />0701 Sine, cosine, tangent and cotangent numeric argument <br />0702 Identical transformation of trigonometric expressions <br />0703 Quadrilateral types and their basic properties <br />0801 Trigonometric and inverse trigonometric functions, their properties <br />0802 Trigonometric equations and inequalities <br />0803 Polygons and their properties <br />0901 The root of n-th degree. Degree of rational parameters <br />0902 The power functions and their properties. Irrational equations, inequalities and their systems <br />0903 Regular polygons and their properties <br />1001 Logarithms. Logarithmic function. Logarithmic equations, inequalities and their systems <br />1002 Exponential function. Indicator of equations, inequalities and their systems <br />1003 Direct and planes in space <br />1101 Derivative and its geometric and mechanical content <br />1102 Derivatives and its application <br />1103 Polyhedron. Prisms and pyramids. Regular polyhedron <br />1201 Initial and definite integral <br />1202 Application of certain integral <br />1203 Body rotation <br />1301 Compounds. Binomial theorem <br />1302 General methods for solving equations, inequalities and their systems <br />1303 Coordinates in the plane and in space <br />1401 The origins of probability theory <br />1402 Beginnings of Mathematical Statistics <br />1403 Vectors in the plane and in space <br /><strong>Maple </strong>version<br /><strong>Html-interactive</strong> version</p><img src="/view.aspx?si=102076/ell.jpg" alt="Exotic EIE-course" align="left"/><p>Ukraine. <br />Exotic training course for the entrance examination in mathematics.<br /><strong>External independent evaluation</strong> <br />Themes:<br />0101 Goals and rational number <br />0102 Interest. The main problem of interest <br />0103 The simplest geometric shapes on the plane and their properties <br />0201 Degree of natural and integral indicator <br />0202 Monomial and polynomials and operations on them <br />0203 Triangles and their basic properties <br />0301 Algebraic fractions and operations on them <br />0302 Square root. Real numbers <br />0303 Circle and circle, their properties <br />0401 Equations, inequalities and their systems <br />0402 Function and its basic properties <br />0403 Described and inscribed triangles <br />0501 Linear function, linear equations, inequalities and their systems <br />0502 Quadratic function, quadratic equation, inequality and their systems <br />0503 Solving square triangles <br />0601 Rational Equations, Inequalities and their sysytemy <br />0602 Numerical sequence. Arithmetic and geometric progression <br />0603 Solving arbitrary triangles <br />0701 Sine, cosine, tangent and cotangent numeric argument <br />0702 Identical transformation of trigonometric expressions <br />0703 Quadrilateral types and their basic properties <br />0801 Trigonometric and inverse trigonometric functions, their properties <br />0802 Trigonometric equations and inequalities <br />0803 Polygons and their properties <br />0901 The root of n-th degree. Degree of rational parameters <br />0902 The power functions and their properties. Irrational equations, inequalities and their systems <br />0903 Regular polygons and their properties <br />1001 Logarithms. Logarithmic function. Logarithmic equations, inequalities and their systems <br />1002 Exponential function. Indicator of equations, inequalities and their systems <br />1003 Direct and planes in space <br />1101 Derivative and its geometric and mechanical content <br />1102 Derivatives and its application <br />1103 Polyhedron. Prisms and pyramids. Regular polyhedron <br />1201 Initial and definite integral <br />1202 Application of certain integral <br />1203 Body rotation <br />1301 Compounds. Binomial theorem <br />1302 General methods for solving equations, inequalities and their systems <br />1303 Coordinates in the plane and in space <br />1401 The origins of probability theory <br />1402 Beginnings of Mathematical Statistics <br />1403 Vectors in the plane and in space <br /><strong>Maple </strong>version<br /><strong>Html-interactive</strong> version</p>102076Mon, 28 Feb 2011 05:00:00 ZTIMOTIMORegression and Data Fitting in Maple
http://www.maplesoft.com/applications/view.aspx?SID=6685&ref=Feed
This application demonstrates Maple's ability to fit data using the LeastSquares command in the CurveFitting package. Several examples are shown, using linear and nonlinear regression.<img src="/view.aspx?si=6685/thumb.GIF" alt="Regression and Data Fitting in Maple" align="left"/>This application demonstrates Maple's ability to fit data using the LeastSquares command in the CurveFitting package. Several examples are shown, using linear and nonlinear regression.6685Mon, 22 Sep 2008 00:00:00 ZMaplesoftMaplesoftAn Interactive Stock Quote Importer
http://www.maplesoft.com/applications/view.aspx?SID=6650&ref=Feed
<p>The Interactive Stock Quote Importer in this worksheet will import quotes (including historical data) from Yahoo for a series of user-specified NYSE stock symbols. This application provides text fields for specifying up to five ticker symbols, allows the user to pick those quantities they want to import with check boxes, summarises the data in a table, and assigns the values to variables for further processing and analysis.</p><img src="/view.aspx?si=6650/thumb.gif" alt="An Interactive Stock Quote Importer" align="left"/><p>The Interactive Stock Quote Importer in this worksheet will import quotes (including historical data) from Yahoo for a series of user-specified NYSE stock symbols. This application provides text fields for specifying up to five ticker symbols, allows the user to pick those quantities they want to import with check boxes, summarises the data in a table, and assigns the values to variables for further processing and analysis.</p>6650Thu, 11 Sep 2008 04:00:00 ZMaplesoftMaplesoftQuality Control of a Paint Production Process
http://www.maplesoft.com/applications/view.aspx?SID=6589&ref=Feed
Quality control in terms of paint production consists of sampling at regular intervals to ensure that the end
product meets a set of target criteria, which include desired yield and concentration levels. These criteria are
determined by developing a model to accurately represent the reaction kinetics of the system. With a highly
accurate model of the chemical process one can quickly identify and correct sources of error during the
production process.<img src="/view.aspx?si=6589/thumb.gif" alt="Quality Control of a Paint Production Process" align="left"/>Quality control in terms of paint production consists of sampling at regular intervals to ensure that the end
product meets a set of target criteria, which include desired yield and concentration levels. These criteria are
determined by developing a model to accurately represent the reaction kinetics of the system. With a highly
accurate model of the chemical process one can quickly identify and correct sources of error during the
production process.6589Thu, 28 Aug 2008 00:00:00 ZMaplesoftMaplesoftBuffon's Needle
http://www.maplesoft.com/applications/view.aspx?SID=6351&ref=Feed
Buffon's needle graphic simulation with Maple<img src="/view.aspx?si=6351/BuffonsNeedle.gif" alt="Buffon's Needle" align="left"/>Buffon's needle graphic simulation with Maple6351Tue, 17 Jun 2008 00:00:00 ZPEDRO GONZALEZPEDRO GONZALEZMultivariate Distributions In Maple
http://www.maplesoft.com/applications/view.aspx?SID=6352&ref=Feed
The document demonstrates the extension of Maple's comprehensive Statistical package into multivariate setting. It shows how Maple's symbolic analytics and numerical engines can be seamlessly applied in the field of multivariate statistics. The core concept of multivariate analysis - joint distributions - are discussed in the context of multivariate Normal distribution and particular aspects of "jointness" are presented through marginal and conditional densities. Extension of multinormality into related family of joint distributions is shown on the example of multivariate Student-t distribution.<img src="/view.aspx?si=6352/thumb2.jpg" alt="Multivariate Distributions In Maple" align="left"/>The document demonstrates the extension of Maple's comprehensive Statistical package into multivariate setting. It shows how Maple's symbolic analytics and numerical engines can be seamlessly applied in the field of multivariate statistics. The core concept of multivariate analysis - joint distributions - are discussed in the context of multivariate Normal distribution and particular aspects of "jointness" are presented through marginal and conditional densities. Extension of multinormality into related family of joint distributions is shown on the example of multivariate Student-t distribution.6352Tue, 17 Jun 2008 00:00:00 ZIgor HlivkaIgor HlivkaStats Calculator
http://www.maplesoft.com/applications/view.aspx?SID=5818&ref=Feed
The worksheet includes transparent codes and maplets with nice interactive plots for three typical models used in the inferential statistics: Standard Normal, Student's t, and Chi-square. Each of the maplets performs the following two tasks:
1. Given a cut-off value (z-value, t-value, or chi-squared ) find the area under the appropriate probability density plot to the LEFT of the cut-off value, and
2. Given an area, find the corresponding cut-off value.
The worksheet can be used as:
Simple tool replacing obsolete statistical tables or "black box" types of software products in teaching introductory statistics courses.
Demonstration of some of the Calculus tools in action in the field of statistics.
Demo of certain document tools and techniques of Maple 10 or 11 (point-and-click technique, authoring maplets, embedded elements, autoexecution).<img src="/view.aspx?si=5818/Untitled-1.gif" alt="Stats Calculator" align="left"/>The worksheet includes transparent codes and maplets with nice interactive plots for three typical models used in the inferential statistics: Standard Normal, Student's t, and Chi-square. Each of the maplets performs the following two tasks:
1. Given a cut-off value (z-value, t-value, or chi-squared ) find the area under the appropriate probability density plot to the LEFT of the cut-off value, and
2. Given an area, find the corresponding cut-off value.
The worksheet can be used as:
Simple tool replacing obsolete statistical tables or "black box" types of software products in teaching introductory statistics courses.
Demonstration of some of the Calculus tools in action in the field of statistics.
Demo of certain document tools and techniques of Maple 10 or 11 (point-and-click technique, authoring maplets, embedded elements, autoexecution).5818Thu, 10 Apr 2008 00:00:00 ZDr. Lydia NovozhilovaDr. Lydia NovozhilovaDecision Analysis using Bayes Rule
http://www.maplesoft.com/applications/view.aspx?SID=5458&ref=Feed
Decision analysis uses conditional probabilities to adjust calculations so that new relevant information (posterior probabilities) can be had. Bayes is a systematic approach to solving decision problems under conditions of uncertainty.<img src="/view.aspx?si=5458//applications/images/app_image_blank_lg.jpg" alt="Decision Analysis using Bayes Rule" align="left"/>Decision analysis uses conditional probabilities to adjust calculations so that new relevant information (posterior probabilities) can be had. Bayes is a systematic approach to solving decision problems under conditions of uncertainty.5458Fri, 26 Oct 2007 00:00:00 ZWayne AllenWayne AllenThe Population of Mexican United States. Part I
http://www.maplesoft.com/applications/view.aspx?SID=4850&ref=Feed
The principal goal of this document is to find mathematical models for the Mexican population
growth since 1921 to 1995 using Maple 10 Statistics and DEtools Pakages and to predict the population for the
2000 and 2005 years.<img src="/view.aspx?si=4850/mexpop.jpg" alt="The Population of Mexican United States. Part I" align="left"/>The principal goal of this document is to find mathematical models for the Mexican population
growth since 1921 to 1995 using Maple 10 Statistics and DEtools Pakages and to predict the population for the
2000 and 2005 years.4850Thu, 14 Dec 2006 00:00:00 ZProf. David Macias FerrerProf. David Macias FerrerRanLip - black-box non-uniform random variate generator
http://www.maplesoft.com/applications/view.aspx?SID=4849&ref=Feed
RanLip is a toolbox for generation of nonuniform random variates from arbitrary Lipschitz-continuous distributions in Maple environment. It uses acceptance/ rejection approach, which is based on approximation of the probability density function from above with a "hat" function. RanLip provides very fast preprocessing and generation times, and yields small rejection constant. It exhibits good performance for up to five variables, and provides the user with a black box nonuniform random variate generator for a large class of distributions, in particular, multimodal distributions.<img src="/view.aspx?si=4849/ranlib.jpg" alt="RanLip - black-box non-uniform random variate generator" align="left"/>RanLip is a toolbox for generation of nonuniform random variates from arbitrary Lipschitz-continuous distributions in Maple environment. It uses acceptance/ rejection approach, which is based on approximation of the probability density function from above with a "hat" function. RanLip provides very fast preprocessing and generation times, and yields small rejection constant. It exhibits good performance for up to five variables, and provides the user with a black box nonuniform random variate generator for a large class of distributions, in particular, multimodal distributions.4849Wed, 13 Dec 2006 00:00:00 ZDr. Gleb BeliakovDr. Gleb BeliakovPolynomial Regression through Least Square Method
http://www.maplesoft.com/applications/view.aspx?SID=4845&ref=Feed
The goals of this document are to show the approximation of a Point Dispersion through Quadratic Regression Polynomials using the Least Square Method and Maple 10 tools.<img src="/view.aspx?si=4845/PolyReg.htm_67.gif" alt="Polynomial Regression through Least Square Method" align="left"/>The goals of this document are to show the approximation of a Point Dispersion through Quadratic Regression Polynomials using the Least Square Method and Maple 10 tools.4845Tue, 21 Nov 2006 00:00:00 ZProf. David Macias FerrerProf. David Macias FerrerStatistics and Data Analysis
http://www.maplesoft.com/applications/view.aspx?SID=1639&ref=Feed
Maple 10 contains a brand new statistics package and new interactive tools for data import and data analysis.
This document covers some of the basic techniques for using the statistics and data analysis tools in Maple 10.<img src="/view.aspx?si=1639/StatisticsAndDataAnalysis_68.gif" alt="Statistics and Data Analysis" align="left"/>Maple 10 contains a brand new statistics package and new interactive tools for data import and data analysis.
This document covers some of the basic techniques for using the statistics and data analysis tools in Maple 10.1639Sun, 26 Jun 2005 04:00:00 ZMaplesoftMaplesoftFitting a Sine Curve to Data
http://www.maplesoft.com/applications/view.aspx?SID=1422&ref=Feed
This worksheet demonstrate making a best sine curve fit to a set of sparse data from observations of the star 51 Pegasi. Also shown is making a best sine curve fit to a set of sparse data from observation of the tides in the Bay of Fundy. The worksheet illustrates nonlinear curve fitting with Maple, using both elementary commands and sophisticated tools.<img src="/view.aspx?si=1422/sinefit_24.gif" alt="Fitting a Sine Curve to Data" align="left"/>This worksheet demonstrate making a best sine curve fit to a set of sparse data from observations of the star 51 Pegasi. Also shown is making a best sine curve fit to a set of sparse data from observation of the tides in the Bay of Fundy. The worksheet illustrates nonlinear curve fitting with Maple, using both elementary commands and sophisticated tools.1422Mon, 10 Jan 2005 00:00:00 ZSteven DunbarSteven DunbarStatistical Analysis with Maple
http://www.maplesoft.com/applications/view.aspx?SID=4594&ref=Feed
Maple 9.5 is a general-purpose environment for performing fast, accurate technical analysis in any field of engineering, science or mathematics.
Maple can greatly facilitate all stages of statistical analysis, including:
- Manipulation of data sets
- Statistical plots
- Descriptive statistics
- Linear and nonlinear regression
- Handling outliers
- Statistical tests<img src="/view.aspx?si=4594/1409.jpg" alt="Statistical Analysis with Maple" align="left"/>Maple 9.5 is a general-purpose environment for performing fast, accurate technical analysis in any field of engineering, science or mathematics.
Maple can greatly facilitate all stages of statistical analysis, including:
- Manipulation of data sets
- Statistical plots
- Descriptive statistics
- Linear and nonlinear regression
- Handling outliers
- Statistical tests4594Mon, 01 Nov 2004 00:00:00 ZMaplesoftMaplesoft