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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.
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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.
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.
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 mathematics, the logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm.The logarithmic norm was independently introduced by Germund Dahlquist [1] and Sergei Lozinskiĭ in 1958, for square matrices.
Where ( ) is the inverse standardized Student t CDF, and ( ) is the standardized Student t PDF. [ 2 ] In probability theory and statistics , Student's t distribution (or simply the t distribution ) t ν {\displaystyle \ t_{\nu }\ } is a continuous probability distribution that generalizes the standard normal distribution .
When k = 1, the Burr distribution is a log-logistic distribution sometimes referred to as the Fisk distribution, a special case of the Champernowne distribution. [ 6 ] [ 7 ] The Burr Type XII distribution is a member of a system of continuous distributions introduced by Irving W. Burr (1942), which comprises 12 distributions.