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Fitting lognormal distributions to data from a size-sorting particle device.
Shulman S; Baron P; Ramsey D
Proceedings of the 2004 American Statistical Association, Section of Physical and Engineering Sciences, Toronto, Ontario, Canada, August 8-12, 2004. Alexandria, VA: American Statistical Association, 2004 Aug; :2084-2089
The cascade impactor is a device for sampling airborne particles to determine the particle mass-weighted aerodynamic-diameter distribution. The particles enter at the top of the device and deposit by decreasing particle diameter on one of the multiple stages or on the final filter. Past experimental data has established the fraction of each particle size expected to deposit on each stage. From the measured masses, estimates of the parameters of the lognormal distribution (either a single distribution or a mixture of two) must be obtained. Procedures based on weighted least squares are evaluated for fitting one or two lognormal distributions to both actual and simulated data. Several different scenarios are considered: 1) geometric means and standard deviations producing one or two modes; 2) distributions with substantial mass either in small, medium, or large particle size stages. For mixtures of two lognormal distributions the weighted least squares solutions can produce imprecise estimates of the lognormal parameters.
Mathematical-models; Air-flow; Air-sampling; Airborne-dusts; Particle-aerodynamics; Particulate-sampling-methods; Air-sampling-equipment; Weight-measurement; Statistical-analysis; Author Keywords: nonlinear optimization
National Institute for Occupational Safety and Health, Division of Applied Research and Technology, 4676 Columbia Parkway, Cincinnati, OH 45226
Proceedings of the 2004 American Statistical Association, Section of Physical and Engineering Sciences, Toronto, Ontario, Canada, August 8-12, 2004
Page last reviewed: September 2, 2020
Content source: National Institute for Occupational Safety and Health Education and Information Division