Formalization of Continuous Probability Distributions

  • Authors:

  • Osman Hasan;Sofiène Tahar

  • Affiliations:

  • Dept. of Electrical & Computer Engineering, Concordia University, 1455 de Maisonneuve W., Montreal, Quebec, H3G 1M8, Canada;Dept. of Electrical & Computer Engineering, Concordia University, 1455 de Maisonneuve W., Montreal, Quebec, H3G 1M8, Canada

  • Venue:
  • CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
  • Year:
  • 2007

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Abstract

Continuous probability distributions are widely used to mathematically describe random phenomena in engineering and physical sciences. In this paper, we present a methodology that can be used to formalize any continuous random variable for which the inverse of the cumulative distribution function can be expressed in a closed mathematical form. Our methodology is primarily based on the Standard Uniform random variable, the classical cumulative distribution function properties and the Inverse Transform method. The paper includes the higher-order-logic formalization details of these three components in the HOL theorem prover. To illustrate the practical effectiveness of the proposed methodology, we present the formalization of Exponential, Uniform, Rayleigh and Triangular random variables.