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Abstract We show for CES demands with heterogeneous productivities that profit, revenue and output distributions lie in the same closed power family as the productivity distribution (e.g., the ‘Pareto circle’). The price distribution lies in the inverse power family. Equilibrium distribution shapes are linked by linear relations between their density elasticities. Introducing product quality decouples the CES circle, and reconciles Pareto price and Pareto sales revenue distributions. We use discrete choice underpinnings to find variable mark-ups for a more flexible demand formulation bridging CES to logit and beyond. For logit demand, exponential (resp. normal) quality-cost distributions generate Pareto (log-normal) economic size distributions.
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Bayesian Non-Parametric Inference for Multivariate Peaks-over-Threshold Models
We consider a constructive definition of the multivariate Pareto that factorizes the random vector into a radial component and an independent angular component. The former follows a univariate Pareto distribution, and the latter is defined on the surface of the positive orthant of the infinity norm unit hypercube. We propose a method for inferring the distribution of the angular component by identifying its support as the limit of the positive orthant of the unit p-norm spheres and introduce a projected gamma family of distributions defined through the normalization of a vector of independent random gammas to the space. This serves to construct a flexible family of distributions obtained as a Dirichlet process mixture of projected gammas. For model assessment, we discuss scoring methods appropriate to distributions on the unit hypercube. In particular, working with the energy score criterion, we develop a kernel metric that produces a proper scoring rule and presents a simulation study to compare different modeling choices using the proposed metric. Using our approach, we describe the dependence structure of extreme values in the integrated vapor transport (IVT), data describing the flow of atmospheric moisture along the coast of California. We find clear but heterogeneous geographical dependence.
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- PAR ID:
- 10523601
- Publisher / Repository:
- Entropy - MDPI
- Date Published:
- Journal Name:
- Entropy
- Volume:
- 26
- Issue:
- 4
- ISSN:
- 1099-4300
- Page Range / eLocation ID:
- 335
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/e26040335
