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Encyclopedia > Exponential power distribution

The exponential power distribution, also known as the generalized error distribution, takes a scale parameter a and exponent b. The probability density is

For b = 1 this reduces to the Laplace distribution. For b = 2 it has the same form as a Gaussian distribution, but with .

Results from FactBites:

 Exponential distribution - Wikipedia, the free encyclopedia (1374 words) The exponential distribution may be viewed as a continuous counterpart of the geometric distribution, which describes the number of Bernoulli trials necessary for a discrete process to change state. An important property of the exponential distribution is that it is memoryless. The conjugate prior for the exponential distribution is the gamma distribution (of which the exponential distribution is a special case).
 Levy skew alpha-stable distribution - Wikipedia, the free encyclopedia (1084 words) Lévy distributions are also found in spectroscopy as a general expression for a quasistatically pressure-broadened spectral line. The power law behavior is evidenced by the straight-line appearance of the PDF for large x, with the slope equal to -(α+1). For α = 1 / 2 and β = 1 the distribution reduces to a Lévy distribution with scale parameter c and shift parameter μ.
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