Recovery of Distributions via Moments

Details

• Personal Author:
  Hakobyan AS ; Mnatsakanov RM
• Description:
  The problem of recovering a cumulative distribution function (cdf) and corresponding density function from its moments is studied. This problem is a special case of the classical moment problem. The results obtained within the moment problem can be applied in many indirect models, e.g., those based on convolutions, mixtures, multiplicative censoring, and right-censoring, where the moments of unobserved distribution of actual interest can be easily estimated from the transformed moments of the observed distributions. Nonparametric estimation of a quantile function via moments of a target distribution represents another very interesting area where the moment problem arises. In all such models one can apply the present results to recover a function via its moments. In this article some properties of the proposed constructions are derived. The uniform rates of convergence of the approximation of cdf, its density function, quantile and quantile density function are obtained as well. [Description provided by NIOSH]
• Subjects:
  Occupational Health Safety
• Keywords:
  Author Keywords: Probabilistic Moment Problem Distribution M-determinate Distribution Moment Recovered Statistical-analysis Uniform Rate Of Convergence
• ISSN:
  0749-2170
• Publisher:
  Institute of Mathematical Statistics
• Document Type:
  Text
• Funding:
  Contract
• Genre:
  Proceedings
• Place as Subject:
  OSHA Region 3 ; West Virginia
• CIO:
  National Institute for Occupational Safety and Health (NIOSH)
• Division:
  HELD - Health Effects Laboratory Division
• Topic:
  Workplace Safety & Health
• Location:
  North America
• Pages in Document:
  252-265
• Volume:
  57
• NIOSHTIC Number:
  nn:20035767
• Citation:
  Optimality: The Third Erich L. Lehmann Symposium, IMS Lecture Notes--Monograph Series. Rojo J, ed. Beachwood, OH: Institute of Mathematical Statistics, 2009 Jan; 57:252-265
• Contact Point Address:
  Robert M. Mnatsakanov, Department of Statistics, West Virginia University, Morgantown, WV 26506
• Email:
  rmnatsak@stat.wvu.edu
• Editor(s):
  Rojo J
• Federal Fiscal Year:
  2009
• Peer Reviewed:
  False
• Source Full Name:
  Optimality: The Third Erich L. Lehmann Symposium, IMS Lecture Notes--Monograph Series
• Collection(s):
  National Institute for Occupational Safety and Health
• Main Document Checksum:
  urn:sha-512:82a0fefaae836f2d84b753302c984b9d62e3ef1aafefd2646e51fb96c15c52e092ad11a9f12803f1302ab8e28371a208109aa1a546b4c158fb9af7b7bb7573ab
• Download URL:
  https://stacks.cdc.gov/view/cdc/187504/cdc_187504_DS1.pdf
• File Type:
  [PDF - 264.06 KB ]