Gamma Distribution ◾ 297
Review Questions
1. What is the relationship that connects the scale and shape parameters of
gamma distribution?
2. How will you estimate the scale parameter, if you can guess the shape param-
eter and have the value of mean of all observations?
3. How will you estimate the scale parameter directly from data?
4. Mention three applications of the gamma distribution.
5. What is the difference between a Poisson process and a gamma process?
Exercises
1. Plot a gamma curve using Excel function GAMMA.DIST for a shape of 3
and a scale of 10 units.
2. Plot a software reliability growth model using gamma distribution with a
scale of 30 days and a shape of 2.2.
3. For the SGRM you have drawn in Exercise 2, calculate the fraction of defects
remaining in the software on day 60. (Clue: use Excel function GAMMA.
INV to calculate the result.)
4. e mean value of a certain data set is 32.2. If the shape factor is estimated
as 3 by seeing the histogram of data, what would be the scale factor of the
gamma distribution of the data?
5. If the mean of data = 12 and the standard deviation is 2, estimate the gamma
shape and scale parameters to obtain a gamma model of data.
References
1. D. Kundu and A. Manglick, Discriminating between the Log-normal and Gamma
Distributions, Faculty of Mathematics and Informatics, University of Passau, Germany.
2. J. F. Lawless, Statistical Models and Methods for Lifetime Data, Wiley, New York, 1982.
3. H. Aksoy, Use of gamma distribution in hydrological analysis, Turkish Journal of
Engineering and Environmental Sciences, 24, 419–428, 2000.
4. G. J. Husak, J. Michaelsen and C. Funk, Use of the gamma distribution to represent
monthly rainfall in Africa for drought monitoring applications, International Journal of
Climatology, 27(7), 935–944, 2007.
5. NIST/SEMATECH Engineering Statistics Handbook, e National Institute of Standards
and Technology (NIST) is an agency of the U.S. Department of Commerce. Available
at http://www.nist.gov /itl/sed/gsg/handbook_project.cfm.
6. S. Meskini, Reliability Models Applied to Smartphone Applications (thesis), e School
of Graduate and Postdoctoral Studies, e University of Western Ontario London,
Ontario, 2013.
7. I. Iervolino and E. Chioccarelli, Gamma modeling of continuous deterioration and
cumulative damage in life-cycle analysis of earthquake-resistant structures, Proceedings
of the 11th Conference on Structural Safety and Reliability, New York, June 16–20, 2013.