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In probability theory and computer science, a log probability is simply a logarithm of a probability. [1] The use of log probabilities means representing probabilities on a logarithmic scale ( − ∞ , 0 ] {\displaystyle (-\infty ,0]} , instead of the standard [ 0 , 1 ] {\displaystyle [0,1]} unit interval .
G. A. Barnard in 1949 coined the commonly used term log-odds; [5] [6] the log-odds of an event is the logit of the probability of the event. [7] Barnard also coined the term lods as an abstract form of "log-odds", [8] but suggested that "in practice the term 'odds' should normally be used, since this is more familiar in everyday life". [9]
In probability and statistics, the log-logistic distribution (known as the Fisk distribution in economics) is a continuous probability distribution for a non-negative random variable. It is used in survival analysis as a parametric model for events whose rate increases initially and decreases later, as, for example, mortality rate from cancer ...
In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis).
The softmax function, also known as softargmax [1]: 184 or normalized exponential function, [2]: 198 converts a vector of K real numbers into a probability distribution of K possible outcomes. It is a generalization of the logistic function to multiple dimensions, and is used in multinomial logistic regression .
Type IV subsumes the other types and is obtained when applying the logit transform to beta random variates. Following the same convention as for the log-normal distribution , type IV may be referred to as the logistic-beta distribution , with reference to the standard logistic function , which is the inverse of the logit transform.
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