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Maximum entropy distributions with quantile information.

Amirsaman H Bajgiran1, Mahsa Mardikoraem2, Ehsan S Soofi2

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European Journal of Operational Research
|August 25, 2020
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Summary
This summary is machine-generated.

This study introduces maximum entropy (ME) models using quantiles to improve probability distributions, offering diagnostics for information utility and a new Asymmetric Laplace distribution. These models enhance expert knowledge integration and risk assessment in various applications.

Keywords:
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Area of Science:

  • Information Theory
  • Probability Theory
  • Statistical Modeling

Background:

  • Quantiles are crucial for probability distributions but traditional methods can introduce non-elicited information or be non-committal.
  • Existing information theory literature primarily focuses on maximum entropy (ME) models based on moment information.

Purpose of the Study:

  • To explore ME models that minimally elaborate uniform and moment-based ME models using quantiles.
  • To provide diagnostics for the utility of quantile information versus moment information.
  • To introduce a new Asymmetric Laplace distribution derived from elaborating the Laplace distribution by quantiles.

Main Methods:

  • Developing ME models that incorporate quantile information as minimum elaborations.
  • Representing ME models with quantiles and moments as mixtures of truncated distributions.
  • Extending information theory to asymmetric linear loss functions.

Main Results:

  • ME models based solely on quantiles facilitate pooling information from multiple experts.
  • The elaboration of the Laplace distribution yields a novel Asymmetric Laplace distribution.
  • Application examples demonstrate comparisons with parametric models, uncertainty measurement, and inventory management adjustments.

Conclusions:

  • ME models incorporating quantiles offer a robust framework for probability distribution development.
  • These models provide valuable diagnostics for assessing information utility and integrating expert knowledge.
  • The newly developed Asymmetric Laplace distribution expands the applicability of ME models to asymmetric loss scenarios.