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I'm a programmer and have a client who annually releases new products which have "long tail" type of sales curves, very heavy when initially released, tapering out until discontinued years later. He wants me to write some software that uses the historical sales to predict what the future demand for the product will be so he can keep proper inventory.

I'm almost positive there's some existing mathematics that will help me with this, but I'm too ignorant of what it might be to sufficiently google in order to learn it.

What branch of mathematics should I study in order to be able to solve my client's problem?

NoChance
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Chuck
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    You should openly tell your client that you're not trained to do what he/she has asked of you because you're not a statistician. The mathematics and statistics needed to do what he wants isn't something you're going to learn in a week and implement.

    But to answer your question, time series and forecasting is the most obvious way to tackle the problem. I imagine you could also fit some probability distribution over your data, but it's nothing one can easily accomplish

     – Sigma Oct 12 '19 at 19:01
  • The relevant branches are probability theory and statistics, specifically the tools of time series, forecasting, and distribution fitting. Implementations of the latter without a good grasp of the foundations of the former is troublesome, beware. For instance, a non-homogeneous Poisson process could model the sales: a decreasing mean rate function (of time) will give higher sales at first that taper off as time goes on (though this won’t incorporate the annual seasonality, so you have to “restart” the process, and the choice of what decreasing rate function to use is its own problem) – Nap D. Lover Oct 12 '19 at 19:12
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    @VictorS. Thanks for the answer, I'll look into that. My client is quite aware that this is new to me, but I do have more of a mathematics background than anyone else he has, and he understands that not only am I confident that I can learn the required skills, I'll have fun doing so. – Chuck Oct 12 '19 at 19:13
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    I suggest you post this question n this: https://stats.stackexchange.com/ You may try to start with a trend curve and move on to determine the best fit to get a good function for each product. See:https://www.youtube.com/watch?v=kW0r1tlmU9U – NoChance Oct 12 '19 at 19:37

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