Estimate of confidence intervals for geometric mean diameter and geometric standard deviation of lognormal size distribution

Confidence of particle size distribution, which is the size distribution of sample particles selected from a large population with lognormal size distribution, has been studied theoretically. Theoretical equations were derived from the basic formulas commonly used in statistics to estimate confidence intervals for geometric mean diameter and geometric standard deviation. Computer simulation has provided size distribution of sample particles by random sampling in order to confirm the theoretical equations. For both geometric mean diameter and geometric standard deviation, the confidence intervals were calculated so that both values of population were placed approximately in the middle of the intervals. The tendencies for the intervals to decrease with an increase in sample particle number and/or significance level, and with a decrease in geometric standard deviation, were reasonable in statistics. The proposed theoretical equations should be useful for estimating confidence of lognormal size distribution.

Graphical abstractConfidence of particle size distribution, which is the size distribution of sample particles selected from a large population with lognormal size distribution, has been studied theoretically. Theoretical equations were derived to estimate confidence intervals for geometric mean diameter and geometric standard deviation. The equations were confirmed by computer simulation. It is found to be useful for estimating confidence of lognormal size distribution.Figure optionsDownload full-size imageDownload as PowerPoint slide