Description
Consider the following distributions:
• continuous uniform distribution between • discrete distribution, that returns the following values with the given probability
Value
Probability 0.2 0.6 0.2
• exponential distribution with average • hyper-exponential distribution with stages, characterized by
= 0.1, = = 0.5)
• hypo-exponential distribution with stages characterized by = 0.1, = 0.2) • Hyper-Erlang characterized by the following branches, number of stages, rates and
selection probabilities
stages
Rate 0.2
Probability 0.1 0.4 0.5
For each distribution, generate = 500 samples using the techniques seen during the course (you use the function that returns uniformly distributed random number of your tool), and plot their approximated CDF the same graph. Also compute, for each of them, the average and the C.V. starting from the generated samples.
OPTIONAL*
Compare for the considered continuous distribution except the Hyper-Erlang, compare the average and the C.V. with the from their analytical expression. Tools like MatLab, already have methods for generating samples from distributions: look for them, and if available, compare the results obtained with such algorithms with the above. Also try replace the internal uniform number generator, with the linear congruential generator algorithm seen during the lesson.
* Optional parts useful challenge your understanding of the topic. You encouraged them, but they will not asked during the exam
