Use the thinning method to sample 10, 000 paths from this process until T = 2. Count how many samples you throw out from each
path, and plot the histogram of those.
Q2 (10 points)
Suppose we have A(t) = 1 + t/2 – 12 /3 + t3 /40 for 0 < t < 2.
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Use the ordered statistics method to sample the interaftival times.
Q3 (20 points)
Suppose we have four days of arrival times where the cycles range from 0 < T < 24, listed in Si. S2, Sa-Sibelow.
Estimate A(t) using the non-parametric method we discussed in class. Plot the shape of A(t) and X (t). Generate 10, 000 samples from
this process; calculate the maximal interarrival time for path, and plot the histogram. If there are no arrivals in a given path, set the
maximum to be 24.
Here we will practice sampling from a homogeneous poison process
Q1 (15 points)
Suppose we have a homogenous Poison process with intensity A = 3. Generate 10, 000 paths up until T = 5, and plot the histogram
of the distribution of the final arrival time. If there are no arrivals, the final arrival time is considered to be zero.
Q1 (15 points)
Suppose we have a homogenous Poison process with intensity 1 = 3. Generate 10, 000 paths up until T = 5, and plot the
of the distribution of the final arrival time. If there are no arrivals, the final arrival time is considered to be zero.
02 (15 points)
Suppose we observe a single run of the homogenous process (see the list S below) and estimate ) from the data. Generate
paths up until T-5, and plot the histogram of the distribution of the minimal interarrival arrival time. If there are no arrive
minimal interarrival time is consider to be T
Q1 (10 points)
Suppose we wish to sample from a non-homogeneous poison process with known intensity N(t) = 5 + exp(-t) for 0 < t < 1 and
At) = 1 + 3t for1 < t < 2.
Use the thinning method to sample 10, 000 paths from this process until T = 2. Count how many samples you throw out from each path,
and plot the histogram of those.
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