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Related Concept Videos

Probability Histograms01:17

Probability Histograms

A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
Probability Distributions01:32

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The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
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Applications of Integration to Probability Density Functions01:27

Applications of Integration to Probability Density Functions

Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF), which...
Cumulative Frequency Distribution01:04

Cumulative Frequency Distribution

A cumulative frequency distribution is another type of frequency distribution. Instead of reporting how many data values fall in some classes, it reports how many data values are contained in either that class or any class to its left. Technically, it means the sum of frequencies of the class and all the classes below it in a frequency distribution. A cumulative frequency is calculated by adding the frequency of each class lower than the corresponding class interval or category. In general, a...
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Poisson Probability Distribution

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
Ogive Graph01:07

Ogive Graph

An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, the cumulative percentages are added to the graph from left to right. An ogive graph plots cumulative frequency on the vertical y-axis and class boundaries along the horizontal x-axis. It’s very similar to a histogram; only instead of rectangles, an ogive displays a single point where the top right of the rectangle would be. Creating this type...

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Trajectory Data Analyses for Pedestrian Space-time Activity Study
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INTERACTIVE VISUALIZATION OF PROBABILITY AND CUMULATIVE DENSITY FUNCTIONS.

Kristin Potter1, Robert M Kirby, Dongbin Xiu

  • 1Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah, 84112, USA.

International Journal for Uncertainty Quantification
|April 2, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a novel visualization system for analyzing complex two-dimensional data fields. The tool aids in understanding stochastic features by interactively displaying probability density functions (PDFs) and cumulative density functions (CDFs).

Keywords:
cumulative density functiongeneralized polynomial chaosprobability density functionstochastic Galerkin methodsstochastic collocation methodsvisualization

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Area of Science:

  • Data Visualization
  • Computational Statistics
  • Scientific Computing

Background:

  • Probability density functions (PDFs) and cumulative density functions (CDFs) are crucial for characterizing random processes and fields.
  • Assessing global stochastic features in two-dimensional fields with spatially varying PDFs is challenging.
  • Existing methods often lack interactive tools for detailed examination of localized statistical information.

Purpose of the Study:

  • To present a new visualization system for exploring two-dimensional data with available PDF/CDF information at each point.
  • To enable users to interactively analyze stochastic properties within complex data fields.
  • To facilitate the understanding of uncertainty quantification in scientific domains like electrophysiology.

Main Methods:

  • Development of a visualization system capable of processing two-dimensional datasets with spatially distributed PDFs.
  • Implementation of a contour display to visualize the normed difference between local PDFs and a user-selected ansatz PDF.
  • Integration of interactive features for on-demand PDF examination at any domain position.

Main Results:

  • The system effectively visualizes the spatial distribution of stochastic information within two-dimensional fields.
  • The contour display provides a clear overview of deviations from a reference PDF.
  • Interactive exploration allows for detailed analysis of local statistical properties.

Conclusions:

  • The developed visualization system offers a powerful approach for analyzing complex stochastic data.
  • It enhances the interpretability of uncertainty quantification results, particularly in fields like electrophysiology.
  • The tool bridges the gap between raw data and actionable statistical insights.