Normalize result to probability density

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Thu, 06/30/2016 - 02:30 am

It is me again, with another question today. If I make a histogram from a wave and tick "Normalize Result to Probability Density", what will be the units of the resulting Y-axis, i.e. how shall I label the Y-axis at the end? Does this opton calculates the probability density of my data, and the correct label for Y-axis is "Probability density"? What actually happens during this "normalization to pobability density" procedure? Is there math for this procedure available somewhere? I can't find anything about it in the Manual or Help. Thanks. Maria
(1) The Igor histogram, when normalized to a pdf, is an estimate of the "true" pdf. As such, its probability integral over the 'x' values is 1, and the units of the histogram must be the inverse of the 'x' units. Igor does not set the units or label automatically, and you will have to label the histogram 'y'-axis units yourself, e.g.
Label left "Probability Density (1/s)"
(2) Note that the histogram probability density shifts the wave scaling so that data correspond to the bin centers. If you use a "sticks-to-zero" graph display the sticks will be bin centered; If you use a bars display the bar LEFT-EDGES will be at the bin centers.
(3) the Probability Density Function math is standard probability theory, available in any basic text (or Wikipedia). In Igor's case, the sum of the pdf Histogram values times the bin width is one, so the pdf Histogram values are obtained from normalization of the original dimensionless (counts) Histogram.

June 30, 2016 at 05:19 am - Permalink