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The log-normal distribution has also been associated with other names, such as McAlister, Gibrat and Cobb–Douglas. [4] A log-normal process is the statistical realization of the multiplicative product of many independent random variables, each of which is positive.
The log-distance path loss model is a radio propagation model that predicts the path loss a signal encounters inside a building or densely populated areas over long distance. While the log-distance model is suitable for longer distances, the short-distance path loss model is often used for indoor environments or very short outdoor distances.
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 product of independent random variables X and Y may belong to the same family of distribution as X and Y: Bernoulli distribution and log-normal distribution. Example: If X 1 and X 2 are independent log-normal random variables with parameters (μ 1, σ 2 1) and (μ 2, σ 2 2) respectively, then X 1 X 2 is a log-normal random variable with ...
If p is a probability, then p/(1 − p) is the corresponding odds; the logit of the probability is the logarithm of the odds, i.e.: = = = = (). The base of the logarithm function used is of little importance in the present article, as long as it is greater than 1, but the natural logarithm with base e is the one most often used.
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. The blue picture illustrates an example of fitting the log-logistic distribution to ranked maximum one-day October rainfalls and it shows the ...
A Poisson compounded with Log(p)-distributed random variables has a negative binomial distribution. In other words, if N is a random variable with a Poisson distribution , and X i , i = 1, 2, 3, ... is an infinite sequence of independent identically distributed random variables each having a Log( p ) distribution, then
The following shows how to implement a location–scale family in a statistical package or programming environment where only functions for the "standard" version of a distribution are available. It is designed for R but should generalize to any language and library.