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Trapezoidal and Simpson’s methods with a random design

Author

Listed:
  • Kaeshammer Thibaud

    (CNRS, Laboratoire de Mathématiques et de leurs applications de Pau fédération IPRA, UMR 5142, Université de Pau et des pays de l’Adour, 64000 Pau, France)

  • Paroissin Christian

    (CNRS, Laboratoire de Mathématiques et de leurs applications de Pau fédération IPRA, UMR 5142, Université de Pau et des pays de l’Adour, 64000 Pau, France)

  • Urmeneta Herna

    (Departamento de Estadística, Informática y matemáticas, Universidad Pública de Navarra, Campus Arrosadía, 31006 Pamplona, Spain)

Abstract

The aim of the present paper is first to propose a state-of-art of this domain. Second, some convergence results are established in the case of the Dirichlet distribution. This distribution has the advantage to include both the uniform case and the deterministic one. In a first part, the Dirichlet distribution is defined and some properties are supplied. In a second part, new results are established in connexion with former theorems.

Suggested Citation

  • Kaeshammer Thibaud & Paroissin Christian & Urmeneta Herna, 2024. "Trapezoidal and Simpson’s methods with a random design," Monte Carlo Methods and Applications, De Gruyter, vol. 30(4), pages 397-411.
    • Handle: RePEc:bpj:mcmeap:v:30:y:2024:i:4:p:397-411:n:1006
    DOI: 10.1515/mcma-2024-2019
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