# Criteria for signal registration [duplicate]

I want to find statistical criteria for signal registration (see pict). When I don't have a signal I registrate a simple gaussian two-dimenshial distribution. When I have a signal I have gaussian plus some "tail" (horizontal on the picture). Direction of a "tail" may differs, but I have some minimum length of a tail for a proper signal.

I tried to use chi square criteria but faild. p-value for my signal was 1.0. What kind of a criteria can I use in this case?

There is a sample data:

A signal:

[[ 0.    0.    0.    0.01  0.01  0.01  0.02  0.01  0.01  0.01  0.    0.    0.  ]
[ 0.    0.    0.01  0.02  0.03  0.05  0.05  0.05  0.03  0.02  0.01  0.    0.  ]
[ 0.    0.01  0.02  0.05  0.09  0.13  0.14  0.13  0.09  0.05  0.02  0.01  0.  ]
[ 0.01  0.02  0.05  0.11  0.2   0.27  0.31  0.28  0.2   0.11  0.05  0.02  0.01]
[ 0.01  0.03  0.09  0.2   0.34  0.48  0.56  0.52  0.37  0.21  0.1   0.03  0.01]
[ 0.01  0.05  0.13  0.27  0.48  0.69  0.84  0.83  0.62  0.4   0.22  0.08  0.03]
[ 0.02  0.05  0.14  0.31  0.54  0.78  0.99  1.    0.77  0.56  0.4   0.29  0.19]
[ 0.01  0.05  0.13  0.27  0.48  0.69  0.84  0.83  0.62  0.4   0.22  0.08  0.03]
[ 0.01  0.03  0.09  0.2   0.34  0.48  0.56  0.52  0.37  0.21  0.1   0.03  0.01]
[ 0.01  0.02  0.05  0.11  0.2   0.27  0.31  0.28  0.2   0.11  0.05  0.02  0.01]
[ 0.    0.01  0.02  0.05  0.09  0.13  0.14  0.13  0.09  0.05  0.02  0.01  0.  ]
[ 0.    0.    0.01  0.02  0.03  0.05  0.05  0.05  0.03  0.02  0.01  0.    0.  ]
[ 0.    0.    0.    0.01  0.01  0.01  0.02  0.01  0.01  0.01  0.    0.    0.  ]]


Not a signal:

[[ 0.    0.    0.    0.01  0.01  0.02  0.02  0.02  0.01  0.01  0.    0.    0.  ]
[ 0.    0.    0.01  0.02  0.04  0.06  0.06  0.06  0.04  0.02  0.01  0.    0.  ]
[ 0.    0.01  0.03  0.06  0.11  0.15  0.17  0.15  0.11  0.06  0.03  0.01  0.  ]
[ 0.01  0.02  0.06  0.14  0.24  0.33  0.37  0.33  0.24  0.14  0.06  0.02  0.01]
[ 0.01  0.04  0.11  0.24  0.41  0.57  0.64  0.57  0.41  0.24  0.11  0.04  0.01]
[ 0.02  0.06  0.15  0.33  0.57  0.8   0.9   0.8   0.57  0.33  0.15  0.06  0.02]
[ 0.02  0.06  0.17  0.37  0.64  0.9   1.    0.9   0.64  0.37  0.17  0.06  0.02]
[ 0.02  0.06  0.15  0.33  0.57  0.8   0.9   0.8   0.57  0.33  0.15  0.06  0.02]
[ 0.01  0.04  0.11  0.24  0.41  0.57  0.64  0.57  0.41  0.24  0.11  0.04  0.01]
[ 0.01  0.02  0.06  0.14  0.24  0.33  0.37  0.33  0.24  0.14  0.06  0.02  0.01]
[ 0.    0.01  0.03  0.06  0.11  0.15  0.17  0.15  0.11  0.06  0.03  0.01  0.  ]
[ 0.    0.    0.01  0.02  0.04  0.06  0.06  0.06  0.04  0.02  0.01  0.    0.  ]
[ 0.    0.    0.    0.01  0.01  0.02  0.02  0.02  0.01  0.01  0.    0.    0.  ]]

• I would consider using mixture analysis for such task. Check this answer of mine. Jan 22, 2015 at 6:09
• I see. I need some time to pluge in it. Jan 22, 2015 at 6:38
• Take your time. Jan 22, 2015 at 7:05
• Am I right that I have to build a model of my "ideal" distribution? If so, the problem is that the direction of a "tail" of my distribution (mentioned avobe) may differ, and I don't see how I could invent an ideal model for this. Thanks. Jan 22, 2015 at 7:19
• No. My idea is the following. Per your description, the distribution, related to the "no signal" situation, is simple Gaussian, hence there is no mixture. Alternatively, you can consider situation with signal presence as a mixture distribution: the original Gaussian and one or more other distributions. Therefore, I think that, by differentiating situations with mixture and without (that's the criteria), you can detect the presence of the signal. Does it make any sense? Jan 22, 2015 at 8:00