Page "Power law" Paragraph 7

Log-normal distributions are often mistaken for power law distributions.

For example, Gibrat's law about proportional growth processes can actually produce limiting distributions that are lognormal, although their log-log plots look linear.

An explanation of this is that although the logarithm of the lognormal density function is quadratic in, yielding a " bowed " shape in a log-log plot, if the quadratic term is small relative to the linear term then the result can appear almost linear.

Therefore a log-log plot that is slightly " bowed " downwards can reflect a log-normal distribution — not a power law.