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    <p>Your formula for the <a href="http://en.wikipedia.org/wiki/Multivariate_normal_distribution" rel="nofollow">multivariate normal distribution</a> is not correct. You have both the <code>sqrt</code> call, <em>and</em> the factor of 1/2 in the power in the coefficient of the exponential. You are also missing the factor of 1/sigma**2 in the exponent.</p> <p>Here's a modified version, using <code>sigma</code> in a way that matches the formula shown in the question:</p> <pre><code>def func(Vz,Vy,Vx): return (1.0/(sigma**2*2*pi)**(3./2)) * exp( - ( ((Vx**2)/2) + ((Vy**2)/2) + ((Vz**2)/2) )/sigma**2 ) </code></pre> <p>After adding a print statement to print the value of <code>sigma</code>, I get:</p> <pre><code>In [28]: run tplquad_question.py sigma = 1 8*integral[0] = 1.00000000196 </code></pre> <p>Edit the script and run again:</p> <pre><code>In [29]: run tplquad_question.py sigma = 2.5 8*integral[0] = 1.00000000927 </code></pre> <p>Here's the complete <code>tplquad_question.py</code>:</p> <pre><code>from __future__ import print_function, division from scipy.integrate import tplquad from numpy import pi, exp, sqrt def func(Vz,Vy,Vx): return (1.0/(sigma**2*2*pi)**(3./2)) * exp( - ( ((Vx**2)/2) + ((Vy**2)/2) + ((Vz**2)/2) )/sigma**2 ) def Vymax(Vx): return sqrt(Vmax**2 - Vx**2) def Vzmax(Vx,Vy): return sqrt(Vmax**2 - Vx**2 - Vy**2) Vmax = 500 sigma = 1 integral = tplquad(func,0,Vmax,lambda a: 0, Vymax,lambda a, y: 0, Vzmax) print("sigma =", sigma) print("8*integral[0] =", 8*integral[0]) </code></pre>
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    1. POUsing scipy integrate tplquad to evaluate triple integral of multivariate gaussian
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    1. USWarren Weckesser
    1. USWarren Weckesser
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    1. COAh, you are correct! Thanks for noticing/pointing that out. Unfortunately, even after correcting that, the output still comes out to a number ~1e-7 so there must be something else going wrong...
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    2. COReally? Could you post your entire code here please? I even tried commenting out my function and replacing it with what you just posted but I still get ~1e-7. Very confusing.
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    3. CO@user23870: I posted my modified version of your script.
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      1. USWarren Weckesser
 

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