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  2. Exponential distribution - Wikipedia

    en.wikipedia.org/wiki/Exponential_distribution

    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 ...

  3. List of probability distributions - Wikipedia

    en.wikipedia.org/wiki/List_of_probability...

    The Dagum distribution; The exponential distribution, which describes the time between consecutive rare random events in a process with no memory. The exponential-logarithmic distribution; The F-distribution, which is the distribution of the ratio of two (normalized) chi-squared-distributed random variables, used in the analysis of variance.

  4. Exponential family - Wikipedia

    en.wikipedia.org/wiki/Exponential_family

    In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a ...

  5. Relationships among probability distributions - Wikipedia

    en.wikipedia.org/wiki/Relationships_among...

    For some distributions, the minimum value of several independent random variables is a member of the same family, with different parameters: Bernoulli distribution, Geometric distribution, Exponential distribution, Extreme value distribution, Pareto distribution, Rayleigh distribution, Weibull distribution. Examples:

  6. Probability distribution - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution

    A discrete probability distribution is the probability distribution of a random variable that can take on only a ... This has an exponential distribution of ...

  7. Boltzmann distribution - Wikipedia

    en.wikipedia.org/wiki/Boltzmann_distribution

    Boltzmann's distribution is an exponential distribution. Boltzmann factor ⁠ ⁠ (vertical axis) as a function of temperature T for several energy differences ε i − ε j.. In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution [1]) is a probability distribution or probability measure that gives the probability that a system will be in a certain ...

  8. Memorylessness - Wikipedia

    en.wikipedia.org/wiki/Memorylessness

    The only memoryless continuous probability distribution is the exponential distribution, shown in the following proof: [9] First, define S ( t ) = Pr ( X > t ) {\displaystyle S(t)=\Pr(X>t)} , also known as the distribution's survival function .

  9. Gumbel distribution - Wikipedia

    en.wikipedia.org/wiki/Gumbel_distribution

    The Gumbel distribution is a particular case of the generalized extreme value distribution (also known as the Fisher–Tippett distribution). It is also known as the log-Weibull distribution and the double exponential distribution (a term that is alternatively sometimes used to refer to the Laplace distribution).