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I am trying to do predictions on plant growth based on cumulative of time series data. Unfortunately I am not a statistician, just a programmer tasked with writing the application that does this (PHP or R) and my last statistics course was well over a decade ago.

I have a time series representing energy. For example (in days, but I also have it in hours and I can even interpolate)

Example data

And I have a little plant that needs between, say, 1200 and 3000 energy units to flower. The probability distribution of this plant flowering may be uniform between 1200 and 3000. Or it may be a normal distribution with mean 2100 and a standard deviation of 450 (the point is that I want to be able to change that distribution function and see what best matches reality).

Now I need some method or formula that gives the the probability that the plant will flower before a certain time, or between two times. For example, what is the chance that the plant will flower before noon on the 5th? Or the probability it will flower on the 7th between 9am and 6pm?

I need some way to take the distribution of the plants required energy values and calculate with it based on dates (using the time series).

Apart from creating a massive table and calculating everything minute-by-minute (or hour-by-hour) by hand, I can't figure out how to do this. There has to be a smarter way using statistics (and PHP or R or something) that I forgot about in the past decade.

Thanks in advance for any help.

Sander Marechal
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    "The probability distribution of this plant flowering may be uniform between 1200 and 3000." Does this mean that, if at a given moment in time a plant accumulates 2100 energy points, then the plant has a 50% probability of flowering? What's your exact question, how to model the energy generation process or the probability of a plant flowering? – mugen Dec 16 '14 at 16:47
  • "Does this mean that, if at a given moment in time a plant accumulates 2100 energy points, then the plant has a 50% probability of flowering?" Yes, that is exactly what I mean. For a uniform distribution it has 0% chance of flowering at 1200 energy, 50% at 2100 energy and 100% at 3000 energy. What I want is some find of R function where I can pass in the energy time-series, a distribution for the required enegry and a datetime, and it gives me back the probability of the plant flowering before that datetime. – Sander Marechal Dec 17 '14 at 07:25

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