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Toward a Unified Approach to Fitting Loss Models

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Jacques Rioux
Jacques Rioux

A systematic approach to fitting loss models.

1 von 33
Toward a unified approach to fitting loss models Jacques Rioux and Stuart Klugman, for presentation at the IAC, Feb. 9, 2004
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The general idea ,[object Object],[object Object],[object Object]
Distributions ,[object Object],[object Object],[object Object],[object Object]
A few familiar distributions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Flexible ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Why mixtures? ,[object Object],[object Object]
Estimating parameters ,[object Object],[object Object],[object Object],[object Object]
Representing the data ,[object Object],[object Object],[object Object]
What is the issue? ,[object Object],[object Object],[object Object],[object Object],[object Object]
Issue – grouped data ,[object Object],[object Object],[object Object]
Review ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example ,[object Object],[object Object],[object Object]
Empirical cdf
Distribution function plot ,[object Object],[object Object]
Example model ,[object Object]
Distribution function plot
Confidence bands ,[object Object],[object Object]
CDF plot with bounds
Other CDF pictures ,[object Object],[object Object]
CDF difference plot
Histogram plot ,[object Object],[object Object]
Histogram plot
Hypothesis tests ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Kolmogorov-Smirnov ,[object Object],[object Object]
Anderson-Darling ,[object Object],[object Object],[object Object],[object Object]
Chi-square test ,[object Object],[object Object]
Results ,[object Object],[object Object],[object Object],[object Object]
Comparing models ,[object Object],[object Object],[object Object]
Several models Model Loglike A-D K-S Chi-sq SBC Exp -628.23 1.2245 0.9739 0.1054 -630.53 Ln -626.26 0.6682 0.9375 0.2126 -630.87 Gam -627.35 0.8369 1.0355 0.2319 -631.96 L/E -623.77 0.2579 0.5829 0.5608 -632.98 G/E -623.64 0.2804 0.5773 0.5260 -632.85 L/E/E -623.39 0.1484 0.4494 0.3472 -637.21 G/E/E -623.26 0.1353 0.4652 0.3348 -637.08
Which is the winner? ,[object Object],[object Object],[object Object],[object Object],[object Object]
Can this be automated? ,[object Object],[object Object],[object Object],[object Object],[object Object]

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Toward a Unified Approach to Fitting Loss Models

  • 1. Toward a unified approach to fitting loss models Jacques Rioux and Stuart Klugman, for presentation at the IAC, Feb. 9, 2004
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  • 20. CDF plot with bounds
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  • 31. Several models Model Loglike A-D K-S Chi-sq SBC Exp -628.23 1.2245 0.9739 0.1054 -630.53 Ln -626.26 0.6682 0.9375 0.2126 -630.87 Gam -627.35 0.8369 1.0355 0.2319 -631.96 L/E -623.77 0.2579 0.5829 0.5608 -632.98 G/E -623.64 0.2804 0.5773 0.5260 -632.85 L/E/E -623.39 0.1484 0.4494 0.3472 -637.21 G/E/E -623.26 0.1353 0.4652 0.3348 -637.08
  • 32.
  • 33.