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On recovering the relative distribution, Part 1: The moment-recovered approach

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  • Mnatsakanov, Robert M.
  • Pommeret, Denys

Abstract

The problems of approximating and estimating the relative distribution of two distributions as well as corresponding density function based on information given by the sequence of so-called transformed (frequency) moments or the scaled values of Laplace transform of the target model are studied. The asymptotic properties of empirical counterparts of proposed constructions are studied and their performances are demonstrated by means of graphs and tables.

Suggested Citation

  • Mnatsakanov, Robert M. & Pommeret, Denys, 2024. "On recovering the relative distribution, Part 1: The moment-recovered approach," Statistics & Probability Letters, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:stapro:v:208:y:2024:i:c:s016771522400004x
    DOI: 10.1016/j.spl.2024.110035
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    References listed on IDEAS

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    1. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
    2. Cwik, Jan & Mielniczuk, Jan, 1993. "Data-dependent bandwidth choice for a grade density kernel estimate," Statistics & Probability Letters, Elsevier, vol. 16(5), pages 397-405, April.
    3. Elodie Brunel & Fabienne Comte & Valentine Genon-Catalot, 2016. "Nonparametric density and survival function estimation in the multiplicative censoring model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 570-590, September.
    4. Pierre-Olivier Goffard & Stéphane Loisel & Denys Pommeret, 2017. "Polynomial Approximations for Bivariate Aggregate Claims Amount Probability Distributions," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 151-174, March.
    5. Elisa–María Molanes-López & Ricardo Cao, 2008. "Relative density estimation for left truncated and right censored data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(8), pages 693-720.
    6. F. Comte & C. Dion, 2016. "Nonparametric estimation in a multiplicative censoring model with symmetric noise," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 768-801, October.
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