The SEVERITY Procedure
- Overview
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Getting Started
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Syntax
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DetailsPredefined DistributionsCensoring and TruncationParameter Estimation MethodParameter InitializationEstimating Regression EffectsLevelization of Classification VariablesSpecification and Parameterization of Model EffectsEmpirical Distribution Function Estimation MethodsStatistics of FitDefining a Severity Distribution Model with the FCMP ProcedurePredefined Utility FunctionsScoring FunctionsCustom Objective FunctionsMultithreaded ComputationInput Data SetsOutput Data SetsDisplayed OutputODS Graphics
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ExamplesDefining a Model for Gaussian DistributionDefining a Model for the Gaussian Distribution with a Scale ParameterDefining a Model for Mixed-Tail DistributionsEstimating Parameters Using Cramér-von Mises EstimatorFitting a Scaled Tweedie Model with RegressorsFitting Distributions to Interval-Censored DataDefining a Finite Mixture Model That Has a Scale ParameterPredicting Mean and Value-at-Risk by Using Scoring FunctionsScale Regression with Rich Regression Effects
- References
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Danielsson, J., de Haan, L., Peng, L., and de Vries, C. G. (2001), “Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation,” Journal of Multivariate Analysis, 76, 226–248.
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Dunn, P. K. and Smyth, G. K. (2005), “Series Evaluation of Tweedie Exponential Dispersion Model Densities,” Statistics and Computing, 15, 267–280.
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Frydman, H. (1994), “A Note on Nonparametric Estimation of the Distribution Function from Interval-Censored and Truncated Observations,” Journal of the Royal Statistical Society, Series B, 56, 71–74.
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Gentleman, R. and Geyer, C. J. (1994), “Maximum Likelihood for Interval Censored Data: Consistency and Computation,” Biometrika, 81, 618–623.
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Greenwood, M. (1926), “The Natural Duration of Cancer,” in Reports of Public Health and Related Subjects, volume 33, 1–26, London: Her Majesty’s Stationery Office.
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Hill, B. M. (1975), “A Simple General Approach to Inference about the Tail of a Distribution,” Annals of Statistics, 3, 1163–1173.
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Jørgensen, B. (1987), “Exponential Dispersion Models (with discussion),” Journal of the Royal Statistical Society, Series B, 49, 127–162.
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Kaplan, E. L. and Meier, P. (1958), “Nonparametric Estimation from Incomplete Observations,” Journal of the American Statistical Association, 53, 457–481.
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Klein, J. P. and Moeschberger, M. L. (1997), Survival Analysis: Techniques for Censored and Truncated Data, New York: Springer-Verlag.
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Klugman, S. A., Panjer, H. H., and Willmot, G. E. (1998), Loss Models: From Data to Decisions, New York: John Wiley & Sons.
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Koziol, J. A. and Green, S. B. (1976), “A Cramér–von Mises Statistic for Randomly Censored Data,” Biometrika, 63, 466–474.
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Lai, T. L. and Ying, Z. (1991), “Estimating a Distribution Function with Truncated and Censored Data,” Annals of Statistics, 19, 417–442.
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Lynden-Bell, D. (1971), “A Method of Allowing for Known Observational Selection in Small Samples Applied to 3CR Quasars,” Monthly Notices of the Royal Astronomical Society, 155, 95–118.
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Searle, S. R. (1971), Linear Models, New York: John Wiley & Sons.
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Turnbull, B. W. (1976), “The Empirical Distribution Function with Arbitrarily Grouped, Censored, and Truncated Data,” Journal of the Royal Statistical Society, Series B, 38, 290–295.
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Tweedie, M. C. K. (1984), “An Index Which Distinguishes between Some Important Exponential Families,” in J. K. Ghosh and J. Roy, eds., Statistics: Applications and New Directions—Proceedings of the Indian Statistical Institute Golden Jubilee International Conference, 579–604.