The exponential distribution is related to a large number of other distributions. CopulaDistribution can be used to build higher-dimensional distributions that contain an exponential distribution, and ProductDistribution can be used to compute a joint distribution with independent component distributions involving exponential distributions. 
TransformedDistribution can be used to represent a transformed exponential distribution, CensoredDistribution to represent the distribution of values censored between upper and lower values, and TruncatedDistribution to represent the distribution of values truncated between upper and lower values. ProbabilityPlot can be used to generate a plot of the CDF of given data against the CDF of a symbolic exponential distribution and QuantilePlot to generate a plot of the quantiles of given data against the quantiles of a symbolic exponential distribution. DistributionFitTest can be used to test if a given dataset is consistent with an exponential distribution, EstimatedDistribution to estimate an exponential parametric distribution from given data, and FindDistributionParameters to fit data to an exponential distribution. The mean, median, variance, raw moments, and central moments may be computed using Mean, Median, Variance, Moment, and CentralMoment, respectively. The probability density and cumulative distribution functions may be given using PDF, x ] and CDF, x ]. Such an assertion can then be used in functions such as Probability, NProbability, Expectation, and NExpectation. Distributed ], written more concisely as x ExponentialDistribution, can be used to assert that a random variable x is distributed according to an exponential distribution. RandomVariate can be used to give one or more machine- or arbitrary-precision (the latter via the WorkingPrecision option) pseudorandom variates from an exponential distribution. The exponential distribution is also used in credit risk modeling, queueing theory, reliability theory, physics, and hydrology. continuous-time counting processes whose increments are independent, stationary, and Poisson-distributed -implemented as PoissonProcess). In stochastic processes, the exponential distribution describes the lengths of interarrival times in homogeneous Poisson processes (i.e. the number of phone calls placed in a specific time interval each day. 
Since then, the exponential distribution has been used to model various phenomena over intervals of approximately constant rate, e.g. Use of the exponential distribution has increased significantly over the last 75 years, due in part to considerable research within the field of order statistics beginning in the early to mid-1950s. in circumstances for which the future lifetime of an individual has the same distribution regardless of its present state. Historically, the exponential distribution has been used most widely to describe events recurring "at random in time", i.e.(This behavior can be made quantitatively precise by analyzing the SurvivalFunction of the distribution.) The exponential distribution is sometimes referred to as the negative exponential distribution, the one-parameter exponential distribution, or the antilogarithmic distribution.
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In addition, the tails of the PDF are "thin", in the sense that the PDF decreases exponentially for large values of. The probability density function (PDF) of an exponential distribution is monotonically decreasing. ExponentialDistribution represents a continuous statistical distribution defined over the interval and parametrized by a positive real number λ.
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