Fortran and MATLAB implementations of the maintain nominal type I error rates well as long as
branch-and-bound algorithm are available as sup- the shape parameter is not too small; even then, the
plemental materials at
http://pubs.amstat.org. results are only slightly conservative. The authors
The generalized Pareto distribution is widely used illustrate the new tests using real applications
to model extreme values such as exceedences over taken from engineering, medicine, and environ-
thresholds in flood data. Existing methods for esti- mental science.
mating parameters have theoretical or computational The issue concludes with “A Technical Note
defects. In “A New and Efficient Estimation Method on ‘Sample Size Determination for Achieving
for the Generalized Pareto Distribution,” Jin Zhang Stability of Double Multivariate Exponentially
and Michael A. Stephens propose a new estimator Weighted Moving Average Controller’,” by
that is computationally easy, free from the problems Sheng-Tsaing Tseng and Bo-Yan Jou. This note is
observed in traditional approaches, and performs a sequel to a recent Technometrics article by Tseng et
well compared to existing estimators. A numeri- al. that presented an explicit formula for determin-
cal example involving heights of waves is used to ing a minimum sample size (needed to construct the
illustrate the various methods, and tests of fit are input-output predicted model) in such a way that
performed to compare them. the asymptotic stability of a double multivariate
The gamma distribution is relevant to exponentially weighted moving average controller
numerous areas of application in the physical, can be achieved with a guaranteed probability. That
environmental, and biological sciences. Dulal K. formula indicates that two key components of the
Bhaumik, Kush Kapur, and Robert D. Gibbons sample size determination are the canonical corre-
present methods for “Testing Parameters of a Gamma lation of input-output variables and the condition
Distribution for Small Samples.” They derive new number of the covariance matrix of input variables.
small sample-based tests for the shape, scale, and This note shows that the goal can be accomplished
mean of the gamma distribution. Simulations are with a reduced sample size that depends on only the
used to study the type I error rates and statistical canonical correlation. n
power of the tests and reveal that the new tests
OCTObER 2009 AMsTAT NEWs 25
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