Comparing the mean vectors of two independent multivariate log-normal distributions

2013 ◽  
Vol 41 (2) ◽  
pp. 259-274 ◽  
Author(s):  
S.H. Lin
2021 ◽  
pp. 21-46
Author(s):  
David Rickard

Framboid size-frequency plots show log-normal distributions with a geometric mean diameter of 6.0 μ‎m and with 95% of framboids ranging between 2.9 and 12.3 μ‎m. The largest framboids may be 250 μ‎m in diameter, although spherical aggregates of framboids, known as polyframboids, may range up to 900 μ‎m in diameter. Various spherical clusters of nanoparticles have been described which are less than 0.2 μ‎m in diameter. These do not form a continuum with framboids. There is no evidence for any significant change in framboid diameters with geologic time, and the differences in mean sizes between hydrothermal and sedimentary framboids do not, at present, appear to be statistically significant. By contrast, it appears that the mean diameters of framboids from non-marine sediments are significantly larger (7.6 μ‎m) than marine framboids (5.7 μ‎m). There is some evidence that framboids formed in the water column are smaller than those formed in sediments, but the non-critical use of this possible difference as a proxy for paleoenvironmental reconstructions is not robust. So-called microframboids and nanoframboids are discrete entities which are distinct from framboids. They are nanoparticle clusters and are not produced by the same processes as those involved in framboid formation, nor do they behave in the same way. They are more akin to atomic clusters, which form similar constructs.


1992 ◽  
Vol 114 (2) ◽  
pp. 76-82 ◽  
Author(s):  
Y. Goda

Statistical variability of a sample of extreme data has been examined by means of Monte Carlo simulations. The Fisher-Tippett types I and II, the Weibull, and the log-normal distributions were chosen for the examination. The sample size covered from 10 to 400, and 10,000 runs were carried out for each combination of sample size, censoring rate, and distribution function. Empirical formulas and tables are presented for the mean and the coefficient of variation of the standard deviation of a sample, the standard deviation of return value, and the confidence interval of return period.


2020 ◽  
Vol 5 (2) ◽  
pp. 187-196
Author(s):  
کامل عبداله نژاد ◽  
علی اکبر جعفری ◽  
نسرین طاطاری ◽  
◽  
◽  
...  

1991 ◽  
Vol 69 (2) ◽  
pp. 293-299 ◽  
Author(s):  
M. Koné ◽  
P. Courtin ◽  
J. Lemerle

Colloidal particles with a c.c.p. structure were obtained from mixtures of antimonic and molybdic acids through a polymerization process. These particles were octahedral and their sizes fits the log-normal distributions. The mean size decreases and the polydispersity increases with increasing Mo content in the particles. The stability of the aqueous dispersions was due to the surface charge density of the particles which was enhanced when increasing the Mo content. Ion exchange reactions can occur with the dispersions. Two different routes lead to Ag+ fixation: substitution of core H+ without flocculation of the dispersion or cancellation of external charges with flocculation. Key words: inorganic exchangers, colloids, antimonic acid, molybdic acid.


1984 ◽  
Vol 93 (6) ◽  
pp. 591-598 ◽  
Author(s):  
Sandeep K Malhotra

Fractals ◽  
2001 ◽  
Vol 09 (04) ◽  
pp. 463-470 ◽  
Author(s):  
WATARU SOUMA

We investigate the Japanese personal income distribution in the high income range over the 112 years (1887–1998), and that in the middle income range over the 44 years (1955–1998). It is observed that the distribution pattern of the log-normal with power law tail is the universal structure. However, the indexes specifying the distribution differ from year to year. One of the index characterizing the distribution is the mean value of the log-normal distribution; the mean income in the middle income range. It is found that this value correlates linearly with the gross domestic product (GDP). To clarify the temporal change of the equality or inequality of the distribution, we analyze Pareto and Gibrat indexes, which characterize the distribution in the high income range and that in the middle income range, respectively. It is found for some years that there is no correlation between the high income and the middle income. It is also shown that the mean value of Pareto index equals to 2, and the change of this index is effected by the change of the asset price. From these analysis, we derive four constraints that must be satisfied by mathematical models.


2020 ◽  
Vol 45 (4) ◽  
pp. 823-831 ◽  
Author(s):  
Søren Wichmann

The terms “language” and “dialect” are ingrained, but linguists nevertheless tend to agree that it is impossible to apply a non-arbitrary distinction such that two speech varieties can be identified as either distinct languages or two dialects of one and the same language. A database of lexical information for more than 7,500 speech varieties, however, unveils a strong tendency for linguistic distances to be bimodally distributed. For a given language group the linguistic distances pertaining to either cluster can be teased apart, identifying a mixture of normal distributions within the data and then separating them fitting curves and finding the point where they cross. The thresholds identified are remarkably consistent across data sets, qualifying their mean as a universal criterion for distinguishing between language and dialect pairs. The mean of the thresholds identified translates into a temporal distance of around one to one-and-a-half millennia (1,075–1,635 years).


Sign in / Sign up

Export Citation Format

Share Document