Bounded lognormal continuous probability distribution.
The bounded lognormal is a continuous probability distribution derived from the lognormal distribution. Unlike the normal and lognormal distributions, its domain has both upper and lower bounds, and it may be either symmetrical or non-symmetrical, depending on its parameters. It therefore may be a good fit for many natural phenomena, for which there are known limits, for example adult male height.
The lognormal probability density function (pdf) f_L is often defined in terms of mu_N and sigma_N, the mean and standard deviation of some normal distribution N.
If we redefine f_L in terms of mode m and standard deviation sigma as f_L', then the bounded lognormal pdf f_BL is the piecewise function:
f_BL(x, m, sigma, upper) =
f_L'(x, m, sigma) for x <= m, and
f_L'(upper-x, upper-m, sigma) for x > m
where the second piece is scaled so that f_BL is continuous at the mode, and (lower, upper) are the lower and upper bounds of the domain.
The bounded lognormal distribution is implemented in Python as an instance of the scipy.stats.rv_continuous class and inherits from it a collection of generic methods.