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Error Estimates in the Sampling From Particle Size Distributions
Author(s) -
Paine Anthony J.
Publication year - 1993
Publication title -
particle and particle systems characterization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.877
H-Index - 56
eISSN - 1521-4117
pISSN - 0934-0866
DOI - 10.1002/ppsc.19930100106
Subject(s) - geometric standard deviation , sampling (signal processing) , standard deviation , mathematics , statistics , particle (ecology) , volume (thermodynamics) , distribution (mathematics) , moment (physics) , particle number , particle size distribution , particle size , sampling error , second moment of area , statistical physics , physics , observational error , mathematical analysis , geometry , thermodynamics , chemistry , optics , classical mechanics , geology , oceanography , detector
It is often necessary to estimate the properties of particle size distributions from limited samples taken from large populations. When the distributions are broad, and higher order moments required, as in the case of volume based particle size distributions, the inferred parameters d 3,50 (volume median diameter) and GSD (geometric standard deviation) can have high intrinsic errors not immediately obvious to the measuring scientist. We show that there is a critical number of particles, N crit , which must be counted or else the error may blow up catastrophically. N crit is very sensitive to the width of the distribution, and is approximately proportional to GSD 11 We develop formulae to estimate the random sampling error inherent in measured values of the d 3,50 and GSD for the log‐normal distribution; compare the predictions to a typical experimental particle size measurement; and then generalize to the median of any arbitrary moment, d r, 50 .