×

Fitting bivariate loss distributions with copulas. (English) Zbl 0931.62044

Summary: Various processes in casualty insurance involve correlated pairs of variables. A prominent example is the loss and allocated loss adjustment expenses on a single claim. In this paper the bivariate copula is introduced and an approach to conducting goodness-of-fit tests is suggested. A large example illustrates the concepts.

MSC:

62H10 Multivariate distribution of statistics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Carriere, J., Dependent decrement theory, Transactions of the society of actuaries, XLVI, 45-74, (1994)
[2] Carriere, J., Testing independence in bivariate distributions of claim frequencies and severities, Insurance: mathematics and economics, 21, 81-89, (1997) · Zbl 0911.62094
[3] Cook, R.; Johnson, M., Generalized burr – pareto – logistic distributions with applications to a uranium exploration data set, Technometrics, 28, 123-131, (1986)
[4] Frees, E.; Carriere, J.; Valdez, E., Annuity valuation with dependent mortality, Journal of risk and insurance, 63, 229-261, (1996)
[5] Frees, E.; Valdez, E., Understanding relationships using copulas, North American actuarial journal, 2, 1-25, (1998) · Zbl 1081.62564
[6] Quesenberry, C., 1986. Some transformation methods in goodness-of-fit. In: D’Agostino, R., Stephens, M., (Eds.), Goodness-of-Fit Techniques, Marcel Dekker, New York: pp. 235-277.
[7] Schwartz, G., Estimating the dimension of a model, Annals of statistics, 6, 461-464, (1978) · Zbl 0379.62005
[8] Turnbull, B.; Weiss, L., A likelihood ratio statistic for testing goodness of fit with randomly censored data, Biometrics, 34, 367-375, (1978) · Zbl 0393.62042
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.