From grouped to de-grouped data: a new approach in distribution fitting for grouped data

ABSTRACT

Sampling within a given interval with a constraint has not been previously considered. Standard parametric simulation engines require knowledge of the parameters of the distribution from which a sample is drawn. These methods are limited if additional constrains are required for the simulated data. We propose a method that generates the targeted number of individual observations within a given interval with a constraint that the average value of observations is known. This method is further extended to a grouped data setting, as a way of data de-grouping, when the frequency and average value of observations are provided for each group. Several simulation studies are employed to evaluate the performance of the proposed method, in case of both a single interval and grouped data, for different simulation settings. Furthermore, the proposed method is evaluated in the parameter recovery when different distributions are fitted to the de-grouped data. This method is found to be superior to the uniform method previously used in data de-grouping. The results of the simulation study are promising and they show that this method can be used successfully in the applications where data de-grouping requires that the average value of observations is maintained in each group. The application of the proposed method is illustrated on a real data of insurance losses for bodily injury claims.

KEYWORDS:

• de-grouping
• grouped data
• acceptance-rejection sampling
• insurance losses

JEL CLASSIFICATIONS:

• C02
• C40
• C60

2010 AMS CLASSIFICATIONS:

• 62F40
• 62P05

Acknowledgements

The authors would like to thank the Associate editor and two referees for their constructive comments and suggestions which have improved the manuscript significantly.

Disclosure statement

No potential conflict of interest was reported by the authors.