Estimation of the size of a finite population in sequatial sampling:truncatedcombinatiorial numbers

Abstract

This note considers the problem of unbiased estimation of the size of a finite population, or the number of equiprobable classes in a population, when sequential sampling plans are aplied. Combinatorial numbers, e.g., Stirling numbers of the second kind or Lah numbers, occurring in sampling distributions when the sample size is fixed, have to be adjusted to take into account the stopping rule. This requires the concept of a truncated combinatorial number, and linearly truncated Stirling numbers and Lah numbers are instances discussed here. UMVU estimators of population size are expressible in terms of ratios of such truncated combiantorial numbers.

Keywords:

• estimation of population size
• sequential sampling
• stopping rule
• truncated combinatorial numbers
• Stirling numbers of the second kind
• Lah numbers