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Mean of Circular Quantities: Mathematics, Mean, Angle, Real number, Directional statistics, Euclidean distance, Unit circle, Polar coordinate system, Arithmetic mean - Softcover

 
9786132891952: Mean of Circular Quantities: Mathematics, Mean, Angle, Real number, Directional statistics, Euclidean distance, Unit circle, Polar coordinate system, Arithmetic mean
Softcover
ISBN 10: 6132891951 ISBN 13: 9786132891952
Publisher: OmniScriptum, 2010

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a mean of circular quantities is a mean which is suited for quantities like angles, daytimes, and fractional parts of real numbers. This is necessary since most of the usual means fail on circular quantities. For example, the arithmetic mean of 0° and 360° is 180°, although 0° would be clearly the better choice. This is one of the simplest examples of statistics of non-Euclidean spaces. Since the arithmetic mean is not effective for angles, the following method can be used to obtain both a mean value and measure for the variance of the angles: Convert all angles to corresponding points on the unit circle. That is convert polar coordinates to Cartesian coordinates. Then compute the arithmetic mean of these points. The resulting point will lie on the unit disk. Convert that point back to polar coordinates

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Reseña del editor

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a mean of circular quantities is a mean which is suited for quantities like angles, daytimes, and fractional parts of real numbers. This is necessary since most of the usual means fail on circular quantities. For example, the arithmetic mean of 0° and 360° is 180°, although 0° would be clearly the better choice. This is one of the simplest examples of statistics of non-Euclidean spaces. Since the arithmetic mean is not effective for angles, the following method can be used to obtain both a mean value and measure for the variance of the angles: Convert all angles to corresponding points on the unit circle. That is convert polar coordinates to Cartesian coordinates. Then compute the arithmetic mean of these points. The resulting point will lie on the unit disk. Convert that point back to polar coordinates

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Publisher
OmniScriptum
Publication date
2010
Language
English
ISBN 10 
6132891951
ISBN 13 
9786132891952
Binding
Tapa blanda
Number of pages
88
Editor
Miller Frederic P., Vandome Agnes F., McBrewster John