One limitation is the increasing uncertainty about the accuracy of the lognormality
of sensitivity in cases of low background exposure levels and correspondingly small incidence values (Crump et al.
Valles, "Flow lognormality
and spatial correlation in crustal reservoirs-I: physical character & consequences for geothermal energy," in Proceedings World Geothermal Congress 2015, p.
A similar result holds for multivariate lognormality
of stochastic variables and aggregate wealth with constant proportional risk aversion on the part of the investor.
To test the normality or lognormality
hypothesis, the Kolmogorov-smirnov test was performed, at 5% of probability.
On sorting, sorting coefficients and lognormality
of the grain size distribution.
The (two-parameter) lognormal distribution has its genesis in the Law of Proportionate Effect, which predicts lognormality
among a population of individuals each of whose income faces the same odds of growing or shrinking by any proportionate rate; the lognormal basically derives from a process of equality of proportionate growth opportunity and deviations from lognormality
may indicate the absence of such opportunity.
It might seem that the assumption of lognormality
is grossly inconsistent with the evidence for stock markets, but much of that evidence is for high-frequency time-series data conditional on prior returns.
It is known that the lognormality
assumption does not hold empirically for stock prices or stock indices.
By the lognormality
assumption, the distribution of the insured-asset-value [V.sub.t] at time t is related to its initial value v at time zero by,
In testing for goodness-of-fit between the actual log distributions and the normal distribution, lognormality
is rejected below the 1% level of significance for C1 to C6, both in 1991 or 2001.
In addition, b can be derived as described below in Equation (2) by assuming lognormality
of the market returns.