Pareto functions are very versatile and a variety of uncertainties can be usefully modelled by them, such as lifetime models in actuarial sciences, survival analysis and growth models in economics, finance, etc. Pareto models play an important role in modelling extreme events. Hosking and Wallis (1987) discussed the parameter and quantile estimation for the generalised Pareto distribution. Optimal experimental designs are used for accurately estimating the unknown parameters of the model. In this study, locally D-, A- and E-optimal designs with two and three support points having equal weights for homoscedastic generalised Pareto, exponentiated Pareto II, and generalised exponentiated Pareto models are obtained. It has also proven that these designs are minimally supported. The results are illustrated through Norwegian fire insurance claim data for the generalised Pareto model. It is found that the D-optimal design with two and three support points is almost the same for equal and unequal weights. It is also observed that the support points for A- and E-optimal designs are the same for all the cases. The designs obtained in the paper can be used in practice.
Author(s)
Details
Poonam Singh
Department of Statistics, University of Delhi, Delhi, India.
Ashok
Kuma
Department of Statistics, University of Lucknow, Lucknow, India.
Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v6/3198
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