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In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln( X ) has a normal distribution.
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.
The log-t distribution has the probability density function: (, ^, ^) = (+) ^ (+ ( ^ ^)) +,where ^ is the location parameter of the underlying (non-standardized) Student's t-distribution, ^ is the scale parameter of the underlying (non-standardized) Student's t-distribution, and is the number of degrees of freedom of the underlying Student's t-distribution. [1]
The modified lognormal power-law (MLP) function is a three parameter function that can be used to model data that have characteristics of a log-normal distribution and a power law behavior. It has been used to model the functional form of the initial mass function (IMF). Unlike the other functional forms of the IMF, the MLP is a single function ...
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
Extreme values like maximum one-day rainfall and river discharge per month or per year often follow a log-normal distribution. [12] The log-normal distribution, however, needs a numeric approximation. As the log-logistic distribution, which can be solved analytically, is similar to the log-normal distribution, it can be used instead.
To derive estimators for the parameters of probability distributions, applying the method of moments to the L-moments rather than conventional moments. In addition to doing these with standard moments, the latter (estimation) is more commonly done using maximum likelihood methods; however using L-moments provides a number of advantages.
The shifted log-logistic distribution is a probability distribution also known as the generalized log-logistic or the three-parameter log-logistic distribution. [ 1 ] [ 2 ] It has also been called the generalized logistic distribution, [ 3 ] but this conflicts with other uses of the term: see generalized logistic distribution .