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Log5 is a method of estimating the probability that team A will win a game against team B, based on the odds ratio between the estimated winning probability of Team A and Team B against a larger set of teams.
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 .
If each team wins in proportion to its quality, A's probability of winning would be 1.25 / (1.25 + 0.8), which equals 50 2 / (50 2 + 40 2), the Pythagorean formula. The same relationship is true for any number of runs scored and allowed, as can be seen by writing the "quality" probability as [50/40] / [ 50/40 + 40/50], and clearing fractions .
The Dirac delta function, although not strictly a probability distribution, is a limiting form of many continuous probability functions. It represents a discrete probability distribution concentrated at 0 — a degenerate distribution — it is a Distribution (mathematics) in the generalized function sense; but the notation treats it as if it ...
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.
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
A probability distribution is not uniquely determined by the moments E[X n] = e nμ + 1 / 2 n 2 σ 2 for n ≥ 1. That is, there exist other distributions with the same set of moments. [4] In fact, there is a whole family of distributions with the same moments as the log-normal distribution. [citation needed]
In probability theory and statistics, the log-Laplace distribution is the probability distribution of a random variable whose logarithm has a Laplace distribution. If X has a Laplace distribution with parameters μ and b, then Y = e X has a log-Laplace distribution. The distributional properties can be derived from the Laplace distribution.