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Moreover, Gaussian logs yield greater accuracy of result than the traditional computing method and help 5-digit log values to be sufficiently accurate for this method. The use of "Gaussians" by Bruce is original in the field of navigation.
The file size distribution of publicly available audio and video data files follows a log-normal distribution over five orders of magnitude. [92] File sizes of 140 million files on personal computers running the Windows OS, collected in 1999. [93] [62] Sizes of text-based emails (1990s) and multimedia-based emails (2000s). [62]
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In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion
In probability theory, a logit-normal distribution is a probability distribution of a random variable whose logit has a normal distribution.If Y is a random variable with a normal distribution, and t is the standard logistic function, then X = t(Y) has a logit-normal distribution; likewise, if X is logit-normally distributed, then Y = logit(X)= log (X/(1-X)) is normally distributed.
ln(r) is the standard natural logarithm of the real number r. Arg(z) is the principal value of the arg function; its value is restricted to (−π, π]. It can be computed using Arg(x + iy) = atan2(y, x). Log(z) is the principal value of the complex logarithm function and has imaginary part in the range (−π, π].
In fact, many other functional forms appear approximately linear on the log–log scale, and simply evaluating the goodness of fit of a linear regression on logged data using the coefficient of determination (R 2) may be invalid, as the assumptions of the linear regression model, such as Gaussian error, may not be satisfied; in addition, tests ...
Of great interest in number theory is the growth rate of the prime-counting function. [3] [4] It was conjectured in the end of the 18th century by Gauss and by Legendre to be approximately where log is the natural logarithm, in the sense that / =