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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 ...
A Gaussian minus exponential distribution has been suggested for modelling option prices. [20] If such a random variable Y has parameters μ , σ , λ , then its negative -Y has an exponentially modified Gaussian distribution with parameters -μ , σ , λ , and thus Y has mean μ − 1 λ {\displaystyle \mu -{\tfrac {1}{\lambda }}} and variance ...
One of the simplest definitions is: The exponential function is the unique differentiable function that equals its derivative, and takes the value 1 for the value 0 of its variable. This "conceptual" definition requires a uniqueness proof and an existence proof, but it allows an easy derivation of the main properties of the exponential function.
In hydrology, the log-normal distribution is used to analyze extreme values of such variables as monthly and annual maximum values of daily rainfall and river discharge volumes. [ 78 ] The image on the right, made with CumFreq , illustrates an example of fitting the log-normal distribution to ranked annually maximum one-day rainfalls showing ...
In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace.It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together along the abscissa, although the term is also sometimes used to refer to ...
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The Erlang distribution is the distribution of a sum of independent exponential variables with mean / each. Equivalently, it is the distribution of the time until the kth event of a Poisson process with a rate of . The Erlang and Poisson distributions are complementary, in that while the Poisson distribution counts the events that occur in a ...
A value of = indicates that the failure rate is constant over time. This might suggest random external events are causing mortality, or failure. The Weibull distribution reduces to an exponential distribution; A value of > indicates that the failure rate increases with time. This happens if there is an "aging" process, or parts that are more ...