Abstract
In data modelling using the composite Pareto distribution, any observations above a particular threshold value are assumed to follow Pareto type distribution, whereas the rest of the observations are assumed to follow a different distribution. This paper proposes on the use of Bayesian approach to the composite Pareto models involving specification of the prior distribution on the proportion of data coming from the Pareto distribution, instead of assuming the prior distribution on the threshold, as often done in the literature. Based on a simulation study, it is found that the parameter estimates determined when using uniform prior on the proportion is less biased as compared to the point estimates determined when using uniform prior on the threshold. Applications on income data and finance are included for illustrative examples.
Highlights
Size-type data may exhibit heavy upper tail property that must be taken into account in statistical modelling
Pareto type distributions have been used successfully to model the distribution of the upper tail [1, 2] but these distributions can only model the observations above a certain threshold and do not take into account of any observations below the threshold value
Composite Pareto models are a family of distribution models that splice the observations into two parts: observations below a threshold value and observations above the threshold, where the threshold is treated as a parameter
Summary
Size-type data may exhibit heavy upper tail property that must be taken into account in statistical modelling. This property of having separate models for observations below and above the threshold value is desirable when the upper tail observations are heavily skewed or believed to be distributed differently compared to the rest of the observations in the data It has found many applications including in the area of insurance [3], survival data [4], internet traffic data [5] and ecology [6]. Other literatures have discussed and used Bayesian analysis for composite Pareto models [7, 8], their approach are tied to specifying prior information on the threshold parameter, not on the proportion of data in the Pareto tail as proposed in this paper.
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