# Lognormal distribution

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## Lognormal distribution

Pattern of frequency of occurrence in which the logarithm of the variable follows a normal distribution. Lognormal distributions are used to describe returns calculated over periods of a year or more.

## Lognormal Distribution

A way to calculate long-term returns on an investment where the natural log of some variable has a normal distribution.
References in periodicals archive ?
The distribution of the data suggested a lognormal distribution of the LOAEL/NOAEL ratio.
"There's the old joke that if you have 10 regular people in a room and Bill Gates walks in, everybody gets a billion dollars richer on average--that's a lognormal distribution," Fox-Kemper says.
Note: BMD, Benchmark Dose; BMDL, Benchmark Dose Lower Confidence Limit; BMDU, Benchmark Dose Upper Confidence Limit; BW, Body Weight; ED50, Effective Dose for a 50% response; LOAEL, Lowest Observed Adverse Effect Level; NOAEL, No Observed Adverse Effect Level; POD, Point of Departure; P50, median of the distribution = Geometric mean of lognormal distribution; P95/P50, ratio between the 95th percentile and the median of the distribution = [(Geometric standard deviation of lognormal distribution).sup.1.6449]; RfD, Reference Dose; SD, Standard Deviation; TD, Toxicodynamic; TK, Toxicokinetic; [UF.sub.L], Uncertainty Factor for LOAEL-to-NOAEL.
It was found that lognormal distribution has the highest average acceptance rates; that is, 14/16 = 87.5%.
For the lognormal distribution, the fluctuation range of the input parameters M and UF are defined in the following equation:
Based on the lognormal distribution of the value ln([tau]), the statistical analysis of the possible influence of the distribution on the main parameters of the KH relaxation peak is made for the first time.
For the overall traffic jam scenario in a dense urban region, the CDF of the Doppler values can be found in Figure 13, which indicate that they tend to follow a lognormal distribution.
In this study, both initial background particles and sources take lognormal distributions, and the background particle size distribution is characterized by its GMD of 500 nm, TPN of 4.34 x [10.sup.1]0 #/[m.sup.3], and GSD of 1.32.
The lognormal distribution has the highest precision in fitting the histogram values, pointing out that collected fingerprints are most likely to be influenced by slow fading due to shadowing.
HbA1c, troponin I, and vitamin D3 follow a lognormal distribution. Their C[V.sub.a], C[V.sub.t], and required number of samples are 0.034, 0.162, and 36 samples, 0.038, 4.1, and 178 samples, and 0.056, 0.581, and 110 samples, respectively.
The default distribution across chemical-specific [TDVF.sub.01] values was fit to a lognormal distribution in [TDVM.sub.01] = [log.sub.10] [TDVF.sub.01] (i.e., In (login [TDVF.sub.01]) is fit to a normal distribution).
Instead, our data were fit best by a lognormal distribution, consistent with the raptors stochastically changing their gaze direction on the basis of accumulated environmental information.
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