Statistics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=234
en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 28 Feb 2017 14:38:42 GMTTue, 28 Feb 2017 14:38:42 GMTNew applications in the Statistics categoryhttp://www.mapleprimes.com/images/mapleapps.gifStatistics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=234
Interactive Country Data Explorer
http://www.maplesoft.com/applications/view.aspx?SID=154181&ref=Feed
This application allows you to choose a set of countries, and then select three of the more than 50 types of statistical data available for those counties, such as life expectancy, literacy rates, health expenditures, and more. You then can visualize how these factors change over time using a BubblePlot. For example, you can select several countries and then visualize how their overall number of internet users has changed along with their gross domestic product, using the x-y axis, while the bubble size shows relative population sizes.<BR><BR>Related MaplePrimes blog post: <A HREF="http://www.mapleprimes.com/maplesoftblog/203857-An-Interactive-Application-For-Exploring">An Interactive Application for Exploring Country Data</A><img src="/view.aspx?si=154181/countrybubble3.PNG" alt="Interactive Country Data Explorer" align="left"/>This application allows you to choose a set of countries, and then select three of the more than 50 types of statistical data available for those counties, such as life expectancy, literacy rates, health expenditures, and more. You then can visualize how these factors change over time using a BubblePlot. For example, you can select several countries and then visualize how their overall number of internet users has changed along with their gross domestic product, using the x-y axis, while the bubble size shows relative population sizes.<BR><BR>Related MaplePrimes blog post: <A HREF="http://www.mapleprimes.com/maplesoftblog/203857-An-Interactive-Application-For-Exploring">An Interactive Application for Exploring Country Data</A>154181Wed, 19 Oct 2016 04:00:00 ZDaniel SkoogDaniel SkoogVisualizing Multiple Datasets with BubblePlot
http://www.maplesoft.com/applications/view.aspx?SID=154178&ref=Feed
The BubblePlot command can convey information about three dimensions of a multi-dimensional dataset using the horizontal axis, the vertical axis, and point (bubble) size. Moreover, if a dataset is a time series, BubblePlot can generate an animation that shows the movement of data points over a common period of time.
In the following example, datasets containing information on Gross Domestic Product at Power Purchasing Parity, Life Expectancy, and Population are retrieved for selected countries and visualized.<img src="/view.aspx?si=154178/BubblePlot.png" alt="Visualizing Multiple Datasets with BubblePlot" align="left"/>The BubblePlot command can convey information about three dimensions of a multi-dimensional dataset using the horizontal axis, the vertical axis, and point (bubble) size. Moreover, if a dataset is a time series, BubblePlot can generate an animation that shows the movement of data points over a common period of time.
In the following example, datasets containing information on Gross Domestic Product at Power Purchasing Parity, Life Expectancy, and Population are retrieved for selected countries and visualized.154178Mon, 17 Oct 2016 04:00:00 ZDaniel SkoogDaniel SkoogGlobal Population from 1804 to 2015
http://www.maplesoft.com/applications/view.aspx?SID=153967&ref=Feed
This worksheet is concerned with the development of the global population during the period of 1804 – 2015, where the population rose from 10^9 to 7.4*10^9. The given data has been interpolated by the cubic spline function. Several nonlinear model functions to data have been suggested and tested by using error norms.<img src="/view.aspx?si=153967/population.png" alt="Global Population from 1804 to 2015" align="left"/>This worksheet is concerned with the development of the global population during the period of 1804 – 2015, where the population rose from 10^9 to 7.4*10^9. The given data has been interpolated by the cubic spline function. Several nonlinear model functions to data have been suggested and tested by using error norms.153967Tue, 09 Feb 2016 05:00:00 ZProf. Josef BettenProf. Josef BettenGlobal Temperature Anomaly
http://www.maplesoft.com/applications/view.aspx?SID=153951&ref=Feed
The temperature anomaly or temperature index is defined as the change from a reference temperature or a long-term mean value. A positive ( negative) anomaly indicates that a measured temperuture is warmer (cooler) than the reference value. In this worksheet anomalies have been based upon the period between 1951 to 1980. We consider especially temperature change from 1980 to 2015.<img src="/view.aspx?si=153951/GlobalTemperature.png" alt="Global Temperature Anomaly" align="left"/>The temperature anomaly or temperature index is defined as the change from a reference temperature or a long-term mean value. A positive ( negative) anomaly indicates that a measured temperuture is warmer (cooler) than the reference value. In this worksheet anomalies have been based upon the period between 1951 to 1980. We consider especially temperature change from 1980 to 2015.153951Tue, 19 Jan 2016 05:00:00 ZProf. Josef BettenProf. Josef BettenFitting Wave Height Data to a Probability Distribution
http://www.maplesoft.com/applications/view.aspx?SID=153864&ref=Feed
<p>The University of Maine records real-time accelerometer data from buoys deployed in the Gulf of Maine and Caribbean (http://gyre.umeoce.maine.edu/buoyhome.php). The data can be downloaded from their website, and includes the significant wave height recorded at regular intervals for the last few months.</p>
<p>This application:</p>
<ul>
<li>downloads accelerometer data for Buoy PR206 (located just off the coast of Puerto Rico at a latitude of 18° 28.46' N and a longitude of 66° 5.94' W),</li>
</ul>
<ul>
<li>fits the significant wave height to a Weibull distribution via two methods: maximum likelihood estimation and moment matching,</li>
</ul>
<ul>
<li>and plots the fitted distributions on top of a histogram of the experimental data</li>
</ul>
<p>The location of buoy PR206 is given in a Google Maps component.</p><img src="/view.aspx?si=153864/distribution.jpg" alt="Fitting Wave Height Data to a Probability Distribution" align="left"/><p>The University of Maine records real-time accelerometer data from buoys deployed in the Gulf of Maine and Caribbean (http://gyre.umeoce.maine.edu/buoyhome.php). The data can be downloaded from their website, and includes the significant wave height recorded at regular intervals for the last few months.</p>
<p>This application:</p>
<ul>
<li>downloads accelerometer data for Buoy PR206 (located just off the coast of Puerto Rico at a latitude of 18° 28.46' N and a longitude of 66° 5.94' W),</li>
</ul>
<ul>
<li>fits the significant wave height to a Weibull distribution via two methods: maximum likelihood estimation and moment matching,</li>
</ul>
<ul>
<li>and plots the fitted distributions on top of a histogram of the experimental data</li>
</ul>
<p>The location of buoy PR206 is given in a Google Maps component.</p>153864Wed, 09 Sep 2015 04:00:00 ZSamir KhanSamir KhanTime Series Analysis: Forecasting Average Global Temperatures
http://www.maplesoft.com/applications/view.aspx?SID=153791&ref=Feed
Maple includes powerful tools for accessing, analyzing, and visualizing time series data. This application works with global temperature data to demonstrate techniques for analyzing time series data sets using the TimeSeriesAnalysis package, including visualizing trends and modeling future global temperatures.<img src="/view.aspx?si=153791/thumb.jpg" alt="Time Series Analysis: Forecasting Average Global Temperatures" align="left"/>Maple includes powerful tools for accessing, analyzing, and visualizing time series data. This application works with global temperature data to demonstrate techniques for analyzing time series data sets using the TimeSeriesAnalysis package, including visualizing trends and modeling future global temperatures.153791Tue, 21 Apr 2015 04:00:00 ZDaniel SkoogDaniel SkoogGenerating random numbers efficiently
http://www.maplesoft.com/applications/view.aspx?SID=153662&ref=Feed
Generating (pseudo-)random values is a frequent task in simulations and other programs. For some situations, you want to generate some combinatorial or algebraic values, such as a list or a polynomial; in other situations, you need random numbers, from a distribution that is uniform or more complicated. In this article I'll talk about all of these situations.<img src="/view.aspx?si=153662/thumb.jpg" alt="Generating random numbers efficiently" align="left"/>Generating (pseudo-)random values is a frequent task in simulations and other programs. For some situations, you want to generate some combinatorial or algebraic values, such as a list or a polynomial; in other situations, you need random numbers, from a distribution that is uniform or more complicated. In this article I'll talk about all of these situations.153662Mon, 18 Aug 2014 04:00:00 ZDr. Erik PostmaDr. Erik PostmaSpectral k-statistics
http://www.maplesoft.com/applications/view.aspx?SID=153618&ref=Feed
<p>The algorithm constructs natural statistics of a spectral sample, by using convolutions on the symmetric group and the Weingarten function. These statistics are unbiased estimators of cumulants of traces.</p><img src="/view.aspx?si=153618/39882f96bb55a4970488a9bcf94fd60d.gif" alt="Spectral k-statistics" align="left"/><p>The algorithm constructs natural statistics of a spectral sample, by using convolutions on the symmetric group and the Weingarten function. These statistics are unbiased estimators of cumulants of traces.</p>153618Thu, 03 Jul 2014 04:00:00 ZDr. Giuseppe GuarinoDr. Giuseppe GuarinoPrincipal Component Analysis
http://www.maplesoft.com/applications/view.aspx?SID=153591&ref=Feed
<p>Principal Component Analysis transforms a multi-dimensional data set to a new set of perpendicular axes (or components) that describe decreasing amounts of variance. </p>
<p>This worksheet reduces the complexity of a data set using principal component analysis. Those components that have the least impact on the variance are discarded, and the simplified data reconstructed from the remaining components.</p><img src="/view.aspx?si=153591/PrincipalComponentAn.jpg" alt="Principal Component Analysis" align="left"/><p>Principal Component Analysis transforms a multi-dimensional data set to a new set of perpendicular axes (or components) that describe decreasing amounts of variance. </p>
<p>This worksheet reduces the complexity of a data set using principal component analysis. Those components that have the least impact on the variance are discarded, and the simplified data reconstructed from the remaining components.</p>153591Mon, 26 May 2014 04:00:00 ZSamir KhanSamir KhanBlutdruckwerte aus Langzeitmessung (Blood Pressure Values)
http://www.maplesoft.com/applications/view.aspx?SID=153556&ref=Feed
<p>During a period of 24 hours the blood pressure of a patient at the University Hospital Aachen has been measured. Thus, we have a lot of Systole-, Diastole-, and Pulse-Values important for a medical doctor treating sick patients. To analyse these “data” the Maple Program 16 (with stats) is very useful.</p>
<p>For graphical representation cubic splines within the Maple Curve Fitting program has been used. In German.</p><img src="/view.aspx?si=153556/16b4d27b4d08cd3278be0fadcf544abd.gif" alt="Blutdruckwerte aus Langzeitmessung (Blood Pressure Values)" align="left"/><p>During a period of 24 hours the blood pressure of a patient at the University Hospital Aachen has been measured. Thus, we have a lot of Systole-, Diastole-, and Pulse-Values important for a medical doctor treating sick patients. To analyse these “data” the Maple Program 16 (with stats) is very useful.</p>
<p>For graphical representation cubic splines within the Maple Curve Fitting program has been used. In German.</p>153556Fri, 25 Apr 2014 04:00:00 ZProf. Josef BettenProf. Josef BettenJump-diffusion stochastic processes with Maple
http://www.maplesoft.com/applications/view.aspx?SID=153516&ref=Feed
<p>The application presents and definition, creation and handling of jump-diffusion processes. In general, jump-diffusion is an extension to the theory of stochastic processes where the underlying parameters exhibit shocks and "jump" to their new values. Stochasticity with jumps is well recognised in several scientific branches including physics, chemistry, biology, but also economic and finance. The application looks at the example of the last-mentioned fields where the theory of jump-diffusions has been particularly actively researched and applied.</p><img src="/view.aspx?si=153516/JD_Process.jpg" alt="Jump-diffusion stochastic processes with Maple" align="left"/><p>The application presents and definition, creation and handling of jump-diffusion processes. In general, jump-diffusion is an extension to the theory of stochastic processes where the underlying parameters exhibit shocks and "jump" to their new values. Stochasticity with jumps is well recognised in several scientific branches including physics, chemistry, biology, but also economic and finance. The application looks at the example of the last-mentioned fields where the theory of jump-diffusions has been particularly actively researched and applied.</p>153516Sat, 08 Mar 2014 05:00:00 ZIgor HlivkaIgor HlivkaIntroduction to Statistics with Maple
http://www.maplesoft.com/applications/view.aspx?SID=149942&ref=Feed
An introduction to statistics and data analysis in Maple including a general overview of statistics. Examples include:
<ul>
<li> Importing data and simple data analysis, including showing Excel connectivity.</li>
<li> Working with Matrix data sets</li>
<li> Working with Random Variables and predefined distributions</li>
<li> Sampling, Monte Carlo & Bootstrapping Techniques</li>
<li> Creating custom distributions</li>
<li> Visualizing data</li>
<li> Hypothesis Testing</li>
<li> Maximum likelihood estimation</li>
<li> And more…</li>
</ul>
These examples were used in a webinar, Maple: Introduction to Statistics. <a href="http://www.maplesoft.com/webinars/recorded/featured.aspx?id=487" target="_blank" >A recording of this webinar is available for viewing</a>.<img src="/view.aspx?si=149942/img.gif" alt="Introduction to Statistics with Maple" align="left"/>An introduction to statistics and data analysis in Maple including a general overview of statistics. Examples include:
<ul>
<li> Importing data and simple data analysis, including showing Excel connectivity.</li>
<li> Working with Matrix data sets</li>
<li> Working with Random Variables and predefined distributions</li>
<li> Sampling, Monte Carlo & Bootstrapping Techniques</li>
<li> Creating custom distributions</li>
<li> Visualizing data</li>
<li> Hypothesis Testing</li>
<li> Maximum likelihood estimation</li>
<li> And more…</li>
</ul>
These examples were used in a webinar, Maple: Introduction to Statistics. <a href="http://www.maplesoft.com/webinars/recorded/featured.aspx?id=487" target="_blank" >A recording of this webinar is available for viewing</a>.149942Mon, 29 Jul 2013 04:00:00 ZDaniel SkoogDaniel SkoogIndependenceModel package
http://www.maplesoft.com/applications/view.aspx?SID=148816&ref=Feed
<p>The main purpose of this work was to write a procedure to implement an algorithm based on the Diaconis Sturmfels algorithm to compute the Monte Carlo p-value of the independence model considered, but we present a package containing also some preliminary commands that can be useful to everyone studying an independence model.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="IndependenceModel package" align="left"/><p>The main purpose of this work was to write a procedure to implement an algorithm based on the Diaconis Sturmfels algorithm to compute the Monte Carlo p-value of the independence model considered, but we present a package containing also some preliminary commands that can be useful to everyone studying an independence model.</p>148816Tue, 25 Jun 2013 04:00:00 ZValentina TrioloValentina TrioloClassroom 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 LopezInterpolation and Smoothing
http://www.maplesoft.com/applications/view.aspx?SID=132223&ref=Feed
These examples illustrate 3-D interpolation and smoothing. It shows the use of a smoothing algorithm to create a smooth surface that approximates your noisy data 3-D data, and interpolation methods that generate a surface that matches your data exactly, regardless of whether the data points lie on a uniform or non-uniform grid. Many of these techniques are new in Maple 16.<img src="/view.aspx?si=132223/thumb.jpg" alt="Interpolation and Smoothing" align="left"/>These examples illustrate 3-D interpolation and smoothing. It shows the use of a smoothing algorithm to create a smooth surface that approximates your noisy data 3-D data, and interpolation methods that generate a surface that matches your data exactly, regardless of whether the data points lie on a uniform or non-uniform grid. Many of these techniques are new in Maple 16.132223Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftStatistics 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 ZMaplesoftMaplesoftMath Apps in Maple
http://www.maplesoft.com/applications/view.aspx?SID=132220&ref=Feed
Math Apps in Maple have give students and teachers the ability to explore and illustrate a wide variety of mathematical and scientific concepts. These fun and easy to use educational demonstrations are designed to illustrate various mathematical and physical concepts. This application contains a sampling of some of the many Math Apps available in Maple: drawing the graph of a quadratic, epicycloids, monte carlo approximations of pi, and throwing coconuts.<img src="/view.aspx?si=132220/mathapps_thumb.png" alt="Math Apps in Maple" align="left"/>Math Apps in Maple have give students and teachers the ability to explore and illustrate a wide variety of mathematical and scientific concepts. These fun and easy to use educational demonstrations are designed to illustrate various mathematical and physical concepts. This application contains a sampling of some of the many Math Apps available in Maple: drawing the graph of a quadratic, epicycloids, monte carlo approximations of pi, and throwing coconuts.132220Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftRegression in Maple
http://www.maplesoft.com/applications/view.aspx?SID=129021&ref=Feed
I have always thought that regressions has been too complicated in Maple. The Fit command is too fiddly ie you have to specify too many things and it is easy to get it wrong plus the statistical output you get is far from mainstream ie you dont get t-values, p-values, R, R^2, Adj R^2 etc etc.
I have therefore designed a new procedure called Reg() which only needs one input and that is a datamatrix.<img src="/view.aspx?si=129021/regression_sm.jpg" alt="Regression in Maple" align="left"/>I have always thought that regressions has been too complicated in Maple. The Fit command is too fiddly ie you have to specify too many things and it is easy to get it wrong plus the statistical output you get is far from mainstream ie you dont get t-values, p-values, R, R^2, Adj R^2 etc etc.
I have therefore designed a new procedure called Reg() which only needs one input and that is a datamatrix.129021Thu, 22 Dec 2011 05:00:00 ZMarcus DavidssonMarcus DavidssonGreat 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 ZAn analysis of Kolmogorov-Smirnov statistics and their distributions
http://www.maplesoft.com/applications/view.aspx?SID=123987&ref=Feed
<p>This worksheet examines the use of Kolomogorov-Smirnov (K-S) statistics and presents MAPLE implementations of their distributions under different conditions and assumptions. The presentation aims at being representative rather than comprehensive, and so may serve as an introduction to the properties and use of K-S statistics. The worksheet draws on existing work listed in the References section, and it implements transcriptions (by the author of this worksheet) of certain algorithms given in a subset of those references. </p><img src="/view.aspx?si=123987/417499\KSstat.JPG" alt="An analysis of Kolmogorov-Smirnov statistics and their distributions" align="left"/><p>This worksheet examines the use of Kolomogorov-Smirnov (K-S) statistics and presents MAPLE implementations of their distributions under different conditions and assumptions. The presentation aims at being representative rather than comprehensive, and so may serve as an introduction to the properties and use of K-S statistics. The worksheet draws on existing work listed in the References section, and it implements transcriptions (by the author of this worksheet) of certain algorithms given in a subset of those references. </p>123987Tue, 19 Jul 2011 04:00:00 ZDr. Melvin BrownDr. Melvin Brown