# How to measure if data conforms to logarithmic curve

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:

• Please edit your question to add these details. – Kodiologist Jul 1 '16 at 17:19
• 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. – whuber Jul 1 '16 at 17:28
• I'm just trying to learn more about data modeling and statistics because I am a programmer. – kinger9120 Jul 1 '16 at 17:29
• 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) – 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.