Statistical Methods for Data Science DATA7202
Semester 2, 2020
Lab 6
1. Consider the nerve data (nerve.csv) from Cox, D. and Lewis, P. (1966). The Sta- tistical Analysis of Series of Events. Chapman & Hall, where the authors reported 799 waiting times between successive pulses along a nerve fiber.
(a) Construct and plot the empirical cdf.
(b) Provide an estimate the fraction of waiting times between 0.4 and 0.6 seconds.
(c) The skewness is a measure of asymmetry of data (or probability distribution). The skewness is given by:
x−μ3 Eσ.
i. Provide (and calculate) a plug-in estimate of the skewness for the nerve data.
ii. Use the bootstrap method to (1000 samples), to provide the 95% confi- dence interval for the skewness.
2. Implement the Tandem Queue example for 1/λ = 3, μ1 = 1, μ2 = 2. Plot a figure of the occupancy of both queues as a function of time. Obtain 95% confidence interval for the following.
• Total time in the system.
• Average waiting time in the first queue.
• Average waiting time in the second queue.
Repeat the analysis for the following parameters; 1/λ = 2.5, 1/λ = 2, and 1/λ = 1.
Objectives
On completion of this laboratory session you should be able to understand and implement the bootstrap method and perform discrete event simulation.
1