The mathematical description of certain breakage mechanisms leading to the logarithmico-normal distribution
作者： Benjamin Epstein
DOI: 10.1016/0016-0032(47)90465-1
关键词: Random variable 、 Normal distribution 、 Combinatorics 、 Central limit theorem 、 Distribution function 、 Statistical physics 、 Mathematics 、 Statistical model 、 Product (mathematics) 、 Product distribution 、 Breakage
摘要: Abstract A number of writers have observed that the particle size distributions obtained from some breakage processes appear to be logarithmico-normal. There been virtually no attempts explain this phenomenon. In paper a statistical model is constructed for mechanism which will generate are asymptotically model, Fn(x), distribution function sizes, after n steps process, product (n + 1) independent random variables and hence, by central limit theorem,
elsevier.com
sci-hub.se 参考文章(5)
J. H. Curtiss, On the Distribution of the Quotient of Two Chance Variables Annals of Mathematical Statistics. ,vol. 12, pp. 409- 421 ,(1941) , 10.1214/AOMS/1177731679
Paul S. Roller, Law of size distribution and statistical description of particulate materials Journal of The Franklin Institute-engineering and Applied Mathematics. ,vol. 223, pp. 609- 633 ,(1937) , 10.1016/S0016-0032(37)91914-8
J. B. Austin, Methods of representing distribution of particle size Industrial & Engineering Chemistry Analytical Edition. ,vol. 11, pp. 334- 339 ,(1939) , 10.1021/AC50134A014
Theodore Hatch, Sarah P. Choate, Statistical description of the size properties of non uniform particulate substances Journal of The Franklin Institute-engineering and Applied Mathematics. ,vol. 207, pp. 369- 387 ,(1929) , 10.1016/S0016-0032(29)91451-4
Paul S. Roller, Statistical Analysis of Size Distribution of Particulate Materials, with Special Reference to Bimodal and Frequency Distributions. Correlation of Quartile with Statistical Values. The Journal of Physical Chemistry. ,vol. 45, pp. 241- 281 ,(1941) , 10.1021/J150407A009