Wind-speed prediction There's an airport which measures wind-speed several times a day and has been doing so for 30 years.
I've plotted a frequency distribution of these values as (how many readings between 0 and 5 mph, how many between 5 and 10 mph and so on). As you might expect, the peak is 5-10 mph and no reading exceeds 50 mph, i.e. they may have strong winds from time to time, but no hurricane has passed through the airport.
The question is - how do I estimate the probability that any given future reading will be more than (say) 75 mph?
 A: Given that you have not observed any speeds greater than 50 and you want to predict the probability of a wind speed greater than 75, the predicted probability will depend greatly on assumptions that you make about how the wind speeds are distributed.  It may be best to try different distributions and assumptions, make predictions from each, and see how similar they are and how they differ.
Parametric approach:
Choose a distribution, since wind speeds cannot be negative a right skewed distribution with non-negative support such as a Gamma, lognormal, or Weibull distribution (or others).  Then fit the distribution to your data (maximum likelihood or other method).  You may need to take non-independence of your data into account in fitting the distribution.  Then make your prediction based on your fitted distribution.
Non-parametric approach:
You can also estimate a distribution using methods like kernel density estimation or log spline estimation (probably others as well) and make predictions based on those.  These are also very dependent on the assumptions/settings that you make.
For the simple case where you want to predict if a new observation will be greater than the current maximum (from an iid sample of size n), the probability is approximately 1/(n+1).
Hope this gives you a good starting point.
