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
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, vol. 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 Statistics: Applications and New Directions—Proceedings of the Indian Statistical Institute Golden Jubilee International Conference, edited by J. K. Ghosh, and J. Roy, 579–604. Calcutta: Indian Statistical Institute.