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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 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.
Gamma distribution, for a non-negative scaling parameter; conjugate to the rate parameter of a Poisson distribution or exponential distribution, the precision (inverse variance) of a normal distribution, etc.
The Weibull distribution reduces to an exponential distribution; A value of k > 1 {\displaystyle k>1\,} indicates that the failure rate increases with time. This happens if there is an "aging" process, or parts that are more likely to fail as time goes on.
If X and Y are independent exponential random variables with mean μ, then X − Y is a double exponential random variable with mean 0 and scale μ. If X i are independent Bernoulli random variables then their parity (XOR) is a Bernoulli variable described by the piling-up lemma. (See also ratio 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 ...
The log-normal distribution is the maximum entropy probability distribution for a random variate X —for which the mean and variance of ln(X) are specified. [ 5 ] Definitions
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 ...