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1.
Summary Independent measurements are taken from distinct populations which may differ in mean, variance and in shape, for instance
in the number of modes and the heaviness of the tails. Our goal is to characterize differences between these different populations.
To avoid pre-judging the nature of the heterogeneity, for instance by assuming a parametric form, and to reduce the loss of
information by calculating summary statistics, the observations are transformed to the empirical characteristic function (ECF).
An eigen decomposition is applied to the ECFs to represent the populations as points in a low dimensional space and the choice
of optimal dimension is made by minimising a mean square error. Interpretation of these plots is naturally provided by the
corresponding density estimate obtained by inverting the ECF projected on the reduced dimension space. Some simulated examples
indicate the promise of the technique and an application to the growth of Mirabilis plants is given. 相似文献
2.
Computation of M. L. estimates for the parameters of a negative binomial distribution from grouped data is considered. For this problem the Scoring, Newton—Raphson and E-M algorithm is derived. Using simulated data the performance of the algorithms is compared with respect to convergence, number of iterations and computing time. Finally an empirical example drawn from actuarial science is given. 相似文献