An Integral Representation for Inverse Moments

D. S. Shibu (), M. R. Irshad () and S. Nadarajah ()
Additional contact information
D. S. Shibu: University College
M. R. Irshad: Cochin University of Science and Technology
S. Nadarajah: University of Manchester

Sankhya A: The Indian Journal of Statistics, 2023, vol. 85, issue 2, No 11, 1394-1402

Abstract: Abstract Inverse moments of discrete random variables are traditionally expressed by summations. But summations are often difficult to simplify. In this note, we derive an integral representation for inverse moments involving the probability generating function, making simplifications a lot easier. Two examples are provided to illustrate the result.

Keywords: Geometric distribution; incomplete beta function; negative binomial distribution; 62E99 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13171-022-00293-4

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