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The Lambert W function, Nuttall’s integral, and the Lambert law

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  • Pakes, Anthony G.

Abstract

This paper offers a new proof that the principal Lambert W-function W(s) is a Bernstein function. The proof derives from a known integral evaluation and leads to a more detailed description of W(s) as a Thorin–Bernstein function with a real-variable description of the Thorin measure, and refinements of some known properties of the Lambert distribution.

Suggested Citation

  • Pakes, Anthony G., 2018. "The Lambert W function, Nuttall’s integral, and the Lambert law," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 53-60.
    • Handle: RePEc:eee:stapro:v:139:y:2018:i:c:p:53-60
    DOI: 10.1016/j.spl.2018.03.015
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    Cited by:

    1. Anthony G. Pakes, 2020. "Self-Decomposable Laws from Continuous Branching Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 361-395, March.
    2. Lóczi, Lajos, 2022. "Guaranteed- and high-precision evaluation of the Lambert W function," Applied Mathematics and Computation, Elsevier, vol. 433(C).

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