How does one determine the percentage of a sample less than or equal to some x value for a set of discrete data that appear to be right-skewed? For example, I have a number of data points, and if I were to draw a curve through them it would look something like this:

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What statistics are most relevant for a sample that appears to be drawn from a right-skewed distribution (suppose we assume that it is from such a distribution based on the result of the sample)? For example, what would be the best measure of deviation for such a distribution? As mentioned by Nick it seems like the negative binomial distribution with a shape parameter $r$ of around 5.

  • $\begingroup$ This question is a little puzzling because computing a CDF would seem to be unrelated to whether the distribution is skewed or not. Are you contemplating some particular form in which the distribution is provided to you? For instance, do you have a formula for the CDF? Or a formula for its PDF? Or the values of some of its moments? Or perhaps just a picture of the graph of a PDF, as provided here? $\endgroup$ – whuber Sep 30 '14 at 16:54
  • $\begingroup$ @whuber Sorry, I think the issue is with how I phrased the question. I'm working to improve that. The idea is that I have gathered data that seems to have a continuous approximation in the form of a right-skewed distribution. $\endgroup$ – 114 Sep 30 '14 at 17:13
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    $\begingroup$ Thank you. Unfortunately that does not completely clear up the vagueness and the last edit adds an additional puzzle. There are two things that must be known to answer this question appropriately: (1) do you wish to estimate properties of the distribution of the population (or process) from which the data are drawn, or do you wish to describe the sample itself? (2) Are you asking how to estimate the population distribution from the sample or not? In the last edit, given that you already have a sample, what do you mean by "gather relevant statistics"? $\endgroup$ – whuber Sep 30 '14 at 17:16
  • $\begingroup$ @whuber I believed initially that I wanted to describe the sample itself, but I think I may be mistaken. Is it a contradiction if by that I mean I want to describe the sample by relating it to a more general (continuous) distribution? I suppose that would suggest I want to estimate population properties in order to get a better idea of what the sample would be like. $\endgroup$ – 114 Sep 30 '14 at 17:26
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    $\begingroup$ If the data are discrete the reference distributions most appropriate are usually themselves discrete (e.g. Poisson, negative binomial). You really need to say more about your data to get better advice. $\endgroup$ – Nick Cox Sep 30 '14 at 17:28

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