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So I have several years of data from a survey. For each year I've used FindDistribution and Predict to see if I can fit the data. Here's one example

enter image description here

Where I used FindDistribution to get 

MixtureDistribution[{0.891801, 0.108199}, {PascalDistribution[12, 0.573172], NegativeBinomialDistribution[16, 0.309136]}]

This is just one year of data, and I've fit all 5 years that I have in a similar way.

What I want to know is if there is anyway to store each year, and to have a prediction for what 2019 will look like. I don't mean forecast, because that seems to extend some sort of continuous treadline. What I mean is there a way to predict what 2019 will look like, based on the data/distributions I've gotten for the previous years?

I've tried using Predict, SystemModeller, and Forecast. When I google this issue I see that it's called predictive analytics, bit I'm a physics graduate that I extremely unfamiliar with these subjects. Any direction or suggestions would be appreciated.

EDIT: The data I'm fitting is the ages of the respondents to the survey on the x axis, with the frequency/number of respondents on the y axis. For all the years that I have, this is what the data looks like on a histogram

enter image description here

FindDistribution was what I used to try to fit each year, but it would be better if there was a way to limit what options it uses. I was trying to use NonlinearModelFit with varying degrees of success (for e.g. you can fit the data from the mean to the max using a power law).

I also have a plot with the PDFs of the distributions over the data here

enter image description here

I can attach each year separately if that would be more useful.

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  • $\begingroup$ It depends on the variability in the fits and what you know. For example, might there be any trends in one or more of the parameters? (That would generally only make sense if the functional form for each year was relatively constant.) Using FindDistribution is a bit of a fishing expedition (in my opinion). Also, maybe it's the 95th percentile from each year that's important. My point is that what to do depends on what you know and the objectives (both of which I don't know from what you've given). Is there a Statistics Consulting Group at your University? $\endgroup$ – JimB Apr 16 at 15:51
  • $\begingroup$ @JimB I've edited my question to show each year, and how the shape remains roughly the same. The number of respondents changes each year. I have no checked if there is a Statistic Consulting Group, but will do. IS there a "better" method than FindDistribution? $\endgroup$ – Jomy Blue Apr 16 at 16:00
  • $\begingroup$ Plotting the PDF's of the estimated distributions on the same graph would be more informative than overlaying histograms. (The histograms vary by the annual total count which I assume is not something of interest.) $\endgroup$ – JimB Apr 16 at 16:14
  • $\begingroup$ @JimB very quickly I already have a plot with PDFs of the distributions as well as the data, for all years. I could do them separately if that would be clearer. $\endgroup$ – Jomy Blue Apr 16 at 16:18
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    $\begingroup$ That looks much better. From 2014 to 2017 there seems to be a slight shift to higher ages and an increase in spread. However, 2018 looks somewhat similar to 2014. Short of sharing your data, my recommendation is to ask the question on stats.stackexchange.com and then come back here for implementation using Mathematica. $\endgroup$ – JimB Apr 16 at 16:33

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