• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.979-991
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• 2022

A special class of exponential dispersion models is the class of Tweedie distributions. This class is very significant in statistical modeling as it includes a number of familiar distributions such as Gaussian, Gamma and compound Poisson. A Tweedie distribution has a power parameter p, a mean m and a dispersion parameter 𝜙. The value of the power parameter lies in identifying the corresponding distribution of the Tweedie family. The basic objective of this research work resides in investigating the existence of the implicit estimator of the power parameter of the Tweedie distribution. A necessary and sufficient condition on the mean parameter m, suggesting that the implicit estimator of the power parameter p exists, was established and we provided some asymptotic properties of this estimator.

• Journal of the Korean Data and Information Science Society
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• v.20 no.3
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• pp.515-526
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• 2009

Pricing based on proper risk has been one of main issues in auto insurance. In this paper, we review how the techniques of pricing in auto insurance have been developed and suggest a better approach which meets the existing risk statistically by comparison. The generalized linear model (GLM) method is discussed for pricing with different distributions. With GLM approach, the distribution of error assumed plays an main role for the best fit corresponding to the characteristics of dependent variables. Tweedie distribution is considered as one of error distributions in addition to widely used Gamma and Poisson distribution. With these different types of error assumption for estimating the proper premium in auto insurance, various modeling approaches are possible. In this paper, various modeling approaches with different assumptions for estimating proper risk is discussed and also real example is given by assuming different.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.227-234
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• 1998

Criteria are derived for the existence of a unique invariant oprobability distribution of a class of nonlinear pth-order autoregressive oprocesses, which reformulate those of Tweedie's. It will be shown that the criteria in this paper are easily applicable to the linear or piecewise linear case so that some of the earlier results are immediate consequences of our main results.

• 한국데이터정보과학회:학술대회논문집
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• 2005.10a
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• pp.85-93
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• 2005

Tweedie (1957a) proposed a method for the analysis of residuals from an inverse Gaussian population paralleling the analysis of variance in normal theory. He called it the analysis of reciprocals. In this paper, we propose a Bayesian model selection procedure based on the fractional Bayes factor for the analysis of reciprocals. Using the proposed model procedures, we compare with the classical tests.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1167-1176
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• 2005

Tweedie (1957a) proposed a method for the analysis of residuals from an inverse Gaussian population paralleling the analysis of variance in normal theory. He called it the analysis of reciprocals. In this paper, we propose a Bayesian model selection procedure based on the fractional Bayes factor for the analysis of reciprocals. Using the proposed model selection procedures, we compare with the classical tests.