330 ◾ Simple Statistical Methods for Software Engineering
Exercises
1. Program Gumbel minimum distribution in Excel. (ere is no readily avail-
able function in Excel.)
2. Program Gumbel maximum distribution in Excel. (ere is no readily avail-
able function in Excel.)
3. In the CSAT Gumbel model with location = 3 and scale = 1, find the risk of
CSAT score falling below 2. Make use the program you have developed for
exercise 1.
4. In the complexity Gumbel maximum model with location = 169 and scale =
87, find the risk of complexity exceeding 300. Make use of the program you
have developed for exercise 1.
5. For schedule variance Gumbel maximum model with location parameter =
20 and scale parameter = 12, find the risk of schedule variance exceeding 40.
References
1. C. Neves and M. I. Fraga Alves, Testing extreme value conditions—An overview and
recent approaches, REVSTAT: Statistical Journal, 6(1), 83–100, 2008.
2. Engineering Statistics Handbook, NIST. http://www.itl.nist.gov/div898/handbook/.
3. J. H. J. Einmahl and S. G. W. R. Smeets, Ultimate 100m World Records rough Extreme-
Value eory, Tilburg University, AZL, Heerlen, July 10, 2009, ISSN 0924-7815.
4. A. A. Zimbidis et al., Modeling earthquake risk via extreme value theory and pric-
ing the respective catastrophe bonds, Astin Bulletin, 37(1), 163–183. doi: 10.2143/
AST.37.1.2020804
©
2007.
5. Y. Lu, T. Nolt, I. Bate and L. Cucu-Grosjean, A Trace-Based Statistical Worst-Case
Execution Time Analysis of Component-Based Real-Time Embedded Systems. IEEE,
Emerging Technologies & Factory Automation (ETFA), 2011 IEEE 16th Conference,
pp. 1–4, Toulouse, 2011.
6. C. Maxim, A. Gogonel, D. Maxim and L. Cucu-Grosjean, Estimation of Probabilistic
Minimum Inter-Arrival Times Using Extreme Value eory, INRIA Nancy-Grand Est,
France. https://hal.inria.fr/hal-00766063/PDF/JW_2012_submitted_26september_v2
.pdf.
7. S. Caires, Extreme Value Analysis: Wave Data, 2011. http://www.jodc.go.jp/info/ioc_doc
/JCOMM_Tech/JCOMM-TR-057.pdf.