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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.
Such variables may be better described by other distributions, such as the log-normal distribution or the Pareto distribution. The value of the normal density is practically zero when the value x {\displaystyle x} lies more than a few standard deviations away from the mean (e.g., a spread of three standard deviations covers all but 0.27 ...
This project work also aims at determining the correct value of density by clearing the objects touching the borders of the image. In this project three applications are taken into account and using Matlab with image processing toolbox the count and density values are calculated for each.
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Another generalized log-logistic distribution is the log-transform of the metalog distribution, in which power series expansions in terms of are substituted for logistic distribution parameters and . The resulting log-metalog distribution is highly shape flexible, has simple closed form PDF and quantile function , can be fit to data with linear ...
In probability theory and statistics, the raised cosine distribution is a continuous probability distribution supported on the interval [, +].The probability density function (PDF) is
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 metalog distribution is a generalization of the logistic distribution, where the term "metalog" is short for "metalogistic".Starting with the logistic quantile function, = = + (), Keelin substituted power series expansions in cumulative probability = for the and the parameters, which control location and scale, respectively.