Hi,
I have a problem in which I need to count the number of (probabilistic) occurrences falling in each non-uniform interval of a distribution.
While the final goal itself can apparently be achieved with histcounts, my problem is upstream, that is with the data about the population to be binned, which is not given by a sample, but by some known parameters about the (entire) population. Here is an exemplification, using packages and their weight to illustrate the problem, which is more general. N.B. I do have the Statistics and Machine Learning toolbox, but I'm not an expert statistician myself.
I have a set of N = 100 packages, and their total weight, W = 1000 kg. Let's say that we know how the weight of packages is distributed (about the mean), and that the variance is also a known, exogenous, parameter. The minimum and maximum weight of the packages in the lot is also known. To recap:
Number of packages N = 100;
Total weight W = 1000 kg;
minimum weight of package wmin = 2 kg;
maximum weight of package wmax = 20 kg;
mean weight = mu = W/N = 1000 kg/100 = 10 kg
variance = sigmacap = 4 (exogenously determined)
distribution of weights about the mean = N(mu,sigmacap) in case of normal distribution
With the above input, how should I proceed in having a (probabilistic) count of how many packages will fall in unqually spaced weight intervals of the type 2-5, 5-10, 10-12, 12-16 and 16-20 kilograms?
Thank you very much for any help or lead you can offer.
Daniele
Best Answer