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The crucial line above is the third. The second follows directly from the definition of expected value. The third line is particular to the categorical distribution, and follows from the fact that, in the categorical distribution specifically, the expected value of seeing a particular value i is directly specified by the associated parameter p ...
The Boltzmann distribution, a discrete distribution important in statistical physics which describes the probabilities of the various discrete energy levels of a system in thermal equilibrium. It has a continuous analogue. Special cases include: The Gibbs distribution; The Maxwell–Boltzmann distribution; The Borel distribution
Download QR code; Print/export Download as PDF; ... Pages in category "Continuous distributions" The following 183 pages are in this category, out of 183 total.
Download QR code; Print/export ... Continuous distributions (3 C, ... Pages in category "Probability distributions" The following 25 pages are in this category, out ...
The shape of a distribution will fall somewhere in a continuum where a flat distribution might be considered central and where types of departure from this include: mounded (or unimodal), U-shaped, J-shaped, reverse-J shaped and multi-modal. [1] A bimodal distribution would have two high points rather than one. The shape of a distribution is ...
The log-likelihood is also particularly useful for exponential families of distributions, which include many of the common parametric probability distributions. The probability distribution function (and thus likelihood function) for exponential families contain products of factors involving exponentiation. The logarithm of such a function is a ...
In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions. It is often used to model the tails of another distribution. It is specified by three parameters: location , scale , and shape .
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).