I have observed an experiment where 500 individuals (one after another) touch surfaces in a room and then leave. So I have a data set of recorded number of surface contacts $n$ for each person. I need to make a pdf of this but not sure how best to do it:

This is a histogram converted to pdf:enter image description here

Would you recommend using a bootstrap sample to calculate the pdf of this distribution by kdensity?


This depends on what you know. If you have subject matter knowledge or theory to suggest a parametric model then the best thing to do is fit the parameters of the model to your data.

If you have no knowledge of the data and want to do density estimation use the original sample. There is nothing to be gained by generating bootstrap samples.

The bootstrap would be useful if you are estimating something from the sample like a population mean, median and standard deviation then bootstrapping to approximate the distribution of the estimate would be appropriate.

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  • $\begingroup$ I see your point. These observed data are to be used in a model which will 'predict' which surfaces are touched by a given person. The downside about the data is that there are gaps missing. eg. no observations were made of people touching 21-23 surfaces. Whereas an outlier exists at 25. Does this change anything would you say when trying to generate a pdf? $\endgroup$ – HCAI Aug 12 '12 at 14:10
  • $\begingroup$ No. If you believe that the data is a random sample from a continuous distribution apply a kernel density estimate to the entire data set. If there is so reason to suspect that the outlier might be an error then try to determine whether or not it should be included. $\endgroup$ – Michael R. Chernick Aug 12 '12 at 14:22
  • $\begingroup$ Thanks. What would be your first way of determining whether that point should be included for not? $\endgroup$ – HCAI Aug 12 '12 at 14:44
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    $\begingroup$ I was just mentioning parameters that can be estimated by bootstrap. The bootstrap is used for medians but not often for means since the central limit theorem usually applies to the sample mean. $\endgroup$ – Michael R. Chernick Aug 12 '12 at 16:34
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    $\begingroup$ There is no statistical method that will help you decide. You would need to investigate how the data were generated to decide. If you are estimating a parameter using the data you would like to know how much influence the outlier has on the estimate. $\endgroup$ – Michael R. Chernick Aug 12 '12 at 16:40

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