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POHow to fit list of 3D data to a 2D normal distribution function (preferably in Python)
 

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  1. POHow to fit list of 3D data to a 2D normal distribution function (preferably in Python)
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    <p>I am looking for any script (preferably Python) to calculate the two dimensional normal distribution function of series of three dimensional data. If one does not exist, I would appreciate any code, or pseudocode, someone could provide.</p> <p>The input will be a list of triples like so</p> <pre><code>[[x1, y1, z1], [x2, y2, z2], [x3, y3, z3],..., [xn, yn, zn]] </code></pre> <p>What I need is the mean and standard deviation/variance of the two dimensional normal distribution that most closely represents the data, so as to be able to manipulate it, and, later, recreate it. </p> <p><strong>example</strong></p> <p>For the sake of simplicity I will defer to using a one dimensional normal function. If I have the following two dimensional data points</p> <pre><code>[ [-4, 0.0001], [-3, 0.0044], [-2, 0.054 ], [-1, 0.242 ], [0 , 0.3989], [1 , 0.242 ], [2 , 0.054 ], [3 , 0.0044], [4 , 0.0001] ] </code></pre> <p>I expect the script to output </p> <pre><code>mean = 0.0 standard deviation = 1.0 variance = 1.0 </code></pre> <p>That way, if I want to, for example, change the standard deviation from <code>sd = 1.0</code> to <code>sd = 2.0</code>, I can modify the curve, recreate it, sample the points <code>-4...4</code>, and rewrite the values to the data like so.</p> <pre><code>[ [-4, 0.027 ], [-3, 0.0648], [-2, 0.121 ], [-1, 0.176 ], [0 , 0.1995], [1 , 0.176 ], [2 , 0.121 ], [3 , 0.0648], [4 , 0.027 ] ] </code></pre> <p>Now my question is: how do I do that with a list of three dimensional points which closely represent a two dimensional normal distribution?</p> <hr> <p>I would prefer to do this in Python, or to call a shell script. However, I would not be against using a program like MatLab or Maple.</p>
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    1. COI don't understand why your 2D data consists of triples. Is your "x" merely an index, as suggested by your 1d example?
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    2. CO@DSM Oops, I guess it's 3D data which I am fitting to a 2D normal distribution (the naming conventions always through me off)
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