I am collecting data that should closely resembles a logarithmic curve. I have many datasets.

How can I measure how closely each dataset resembles a logarithmic curve and call out any outlying data points?

Here is an example of a curve that would represent my dataset:

enter image description here

  • $\begingroup$ Please edit your question to add these details. $\endgroup$ – Kodiologist Jul 1 '16 at 17:19
  • $\begingroup$ Because this image does not look at all like what most people would understand a "logarithmic curve" to be, please explain what you mean by this term. Additional details of your data would be helpful, such as the total numbers of counts (not just their average per second) and any other information about how and why the values might vary. $\endgroup$ – whuber Jul 1 '16 at 17:28
  • $\begingroup$ I'm just trying to learn more about data modeling and statistics because I am a programmer. $\endgroup$ – kinger9120 Jul 1 '16 at 17:29
  • $\begingroup$ In this example I am trying to measure the speed at which a component is moving in a video. It moves quickly then slowly comes to a stop. In my dataset I have 200-300 datapoints (About 60 per second) $\endgroup$ – kinger9120 Jul 1 '16 at 17:31

There's an easy, non-statistical approach to the problem of measuring the speed of an object for which you have high-resolution position information like this. Say $x$ is a vector of (one-dimensional) positions and $t$ is a vector of times, such that after $t_i$ seconds have passed, the object is at $x_i$. You can estimate the object's speed at any time $t_i$ as $(x_{i+1} - x_i)/(t_{i+1} - t_i)$. The resemblance of this formula to the derivative of $x$ with respect to $t$ is not coincidental.

  • $\begingroup$ Could you indicate what aspect of the post indicates these are "high-resolution" data? The framerate isn't really relevant, because what matters is the framerate relative to the speeds of the objects. This may be an important issue, because the estimator you propose relies for its accuracy on the assumption of high (temporal) resolution--there are better ones available, depending on how smoothly the objects move. $\endgroup$ – whuber Jul 1 '16 at 17:50
  • $\begingroup$ I say "high-resolution" because OP has 60 measurements per second. I gather the object is moving slowly enough that it takes at least a few seconds to get across the screen, since OP says they have 200 to 300 datapoints. $\endgroup$ – Kodiologist Jul 1 '16 at 17:57
  • $\begingroup$ What other estimators could I look into whuber? $\endgroup$ – kinger9120 Jul 1 '16 at 19:53

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