By J. Aitchison (auth.), Charles Taillie, Ganapati P. Patil, Bruno A. Baldessari (eds.)
Read Online or Download Statistical Distributions in Scientific Work: Volume 4 — Models, Structures, and Characterizations, Proceedings of the NATO Advanced Study Institute held at the Università degli Studi di Trieste, Trieste, Italy, July 10 – August 1, 1980 PDF
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35 HYPERBOLIC DISTRIBUTIONS ACKNOWLEDGEMENT We are grateful to D. R. :\. REFERENCES Abramowitz, M. and Stegun, I. A. (1965). Handbook of Mathematical Functions. Dover, New York. Barndorff-Nielsen, O. (1978a). Hyperbolic distributions and distribution on hyperbolae. Scandinavian Journal of Statistics,S, 151-157. Barndorff-Nielsen, O. (1978b). Information and Exponential Families. Wiley, Chichester. Barndorff-Nielsen, O. (1979). Hyperbolic likelihood. Research Report No. 45, Department of Theoretical Statistics, Aarhus University (to appear in Festschrift to C.
If the imprecision is appreciable standard procedures, such as NewtonRaphson iteration for estimating a, which work readily under the assumption of precise data, fail completely for the degree of imprecision actually present. provides a similar modelling process for the problem of calibration when there is imprecision in the features. 2 Statistical Diagnosis From Imprecise TYPes. There are a number of diagnostic problems where even the cases in the training set are not diagnosed with certainty but where, for each case, probabilities of the possible types in T have been assigned.
O. BARNDORFF-NIELSEN AND P. BLAESILD 30 cases for which neither the parameter method are suitable. w nor the numerical In order to indicate the shape of the log-likelihood function the partially maximized log-likelihood function for nand ~ for one of the samples with n = 40 is shown in Figure 5. S "i -, FIG. 25. 0, ... 5, as indicated on the figure. 52). 4. APPROXIMATION BY (GENERALIZED) HYPERBOLIC DISTRIBUTIONS It may occasionally be of interest to approximate a theoretical probability distribution by one of the hyperbolic or generalized hyperbolic distributions.