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In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
The q-deformed exponential and logarithmic functions were first introduced in Tsallis statistics in 1994. [1] However, the q -logarithm is the Box–Cox transformation for q = 1 − λ {\displaystyle q=1-\lambda } , proposed by George Box and David Cox in 1964.
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Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Help ... Marshall–Olkin exponential distribution;
Diagram showing queueing system equivalent of a hyperexponential distribution. In probability theory, a hyperexponential distribution is a continuous probability distribution whose probability density function of the random variable X is given by = = (),
In applied statistics, the Marshall–Olkin exponential distribution is any member of a certain family of continuous multivariate probability distributions with positive-valued components. It was introduced by Albert W. Marshall and Ingram Olkin . [ 1 ]
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The cross-entropy pendant is the expectation of the negative q-logarithm with respect to a second distribution, .So ().. Using =, this may be written ([]) /.For smaller , values all tend towards .