Exponential Distribution


Also found in: Dictionary, Medical, Wikipedia.

exponential distribution

[‚ek·spə′nen·chəl dis·trə′byü·shən]
(statistics)
A continuous probability distribution whose density function is given by ƒ(x) = ae -ax,where a > 0 for x > 0, and ƒ(x) = 0 for x ≤ 0; the mean and standard deviation are both 1/ a.

Exponential Distribution

 

a probability distribution on the real line. When x ≥ 0, the distribution’s probability density p(x) is equal to the exponential function λex, where λ > 0 (hence the name of the distribution). When x < 0, p(x) = 0. The probability that a random quantity x having an exponential distribution will assume values exceeding some arbitrary number x is equal to ex. The mathematical expectation and variance of x are equal to 1/λ and 1/λ2, respectively.

The exponential distribution is the only continuous probability distribution with the property of absence of aftereffect—that is, for any values x1 and x2, the equation

P (X > x1 + x2) = P (X > x1)P (X > x2)

is satisfied. This characteristic property largely explains, for example, the role that the exponential distribution plays in problems of queuing theory, where the assumption of the exponential distribution of service time is natural. The exponential distribution is closely associated with the concept of a Poisson process. The intervals between successive events in such a process are independent random quantities that have an exponential distribution; here λ is equal to the average number of events per unit time.

REFERENCE

Feller, W. Vvedenie v teoriiu veroiatnostei i eeprilozheniia, 2nd ed., vols. 1-2. Moscow, 1967. (Translated from English.)

A. V. PROKHOROV

References in periodicals archive ?
3.2.a Definition: Neutrosophic exponential distribution [21] is defined as a generalization of classical exponential distribution, Neutrosophic exponential distribution can deals with all the data even non-specific, we express the density function as:
The time interval between every step follows [beta] parameter exponential distribution.
Prediction intervals for the two parameter exponential distribution. Technometrics, 19(4), 469-472.
The pore distribution in pore statistical model is uniform and the pore size distribution is exponential distribution. The pore size distribution function is expressed as
And under the approximation of negative exponential distribution with lambdab = 0.007114, the decay of pdf looks more rapid than that of Figure 3(a).
We find that the risk premium with the Exponential distribution is negative more times than with the Normal distribution.
After the measure transform, the jumps have an exponential distribution with density function [F.sup.*](dx) = ([eta] + 1)[e.sup.([eta]+1)x], arriving at rate [[lambda].sup.*] = [lambda][eta]/([eta]+1) under the probability measure [Q.sup.*].
Assume that the loops of the replicas are independent and each of them follows an exponential distribution with parameter [[lambda].sub.s] and [[lambda].sub.s] > 0.
In addition, it is shown that this optimal order quantity is bigger than EPM order quantity for both high-profit and low-profit products when market demand follows the exponential distribution. Recall that both the experiments in Schweitzer and Cachon [19] assumed that the market demand is uniformly distributed and the results are examined in such an environment.
Then each mobile terminal generates a random number following exponential distribution [20], and its mean equals E which is predefined.
The convolution of a Gaussian distribution and a negative exponential distribution is known as the exponentially modified Gaussian (EMG).
The scale parameter is the same scale parameter of the exponential distribution describing the prime gaps.