I have ten years of data, which I have averaged. Is it possible to calculate the probability that a future point we be less than a threshold based on my data?
For example, say the average is 0.065. How can I calculate the probability, P, that a future data point will be less than 0.1? I am looking at daily data points, where each day is an average of the daily data for the previous ten years.
I understand I may need something other than the average, like a distribution it something, but I do not know what that is. Depending on how specific an answer is, I can look up equations and formulas.
Thanks.
Best Answer
You can get some useful data if you assume that your 10 years of daily data are independant and of identical distribution.
In that case, your best estimator of the probability of a measurement to be lower than 0.1 is :
$\frac{n}{N}$
where $n$ is the number of observations lower than $0.1$ and $N$ the total number of observations.
Yes, it's that simple. Please be aware that the devil is in the hypothesis, as usual in statistics.
More complex models would try to derive the distribution of your observations in a fixed set of distributions.
Even more complex model would state that the observations are not independant and identically distribued, but this is a much wider area.