Approximating an unknown distribution when distribution information is extremely limited

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Abstract

When distribution information is extremely limited, mean-squared-errors (MSEs) of sample estimates may be too large to allow for satisfactory application of traditional distribution-fitting procedures. In particular, sample estimates of skewness and kurtosis are associated with large MSEs. In this paper, new procedures that require estimates of only low degree moments (second degree, at most) are developed under various data- availability scenarios. In particular, procedures are developed for left and right censoring. Using Monte-Carlo simulation for a representative set of cases, we show that moment-estimates derived from distributions fitted by the new procedures generally have MSEs smaller than those of corresponding estimates based on sample moments.

Original languageEnglish
Pages (from-to)501-523
Number of pages23
JournalCommunications in Statistics Part B: Simulation and Computation
Volume27
Issue number2
DOIs
StatePublished - 1 Jan 1998

Keywords

  • Approximations
  • Censored-data
  • Distribution-fitting
  • Moments

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