Description Details Author(s) References See Also

Explanation of Euler's Constant.

Euler's Constant, here denoted *ε*, is a real-valued number that can
be defined in several ways. Johnson et al. (1992, p. 5) use the definition:

*ε = \lim_{n \to ∞}[1 + \frac{1}{2} + \frac{1}{3} + … + \frac{1}{n} - log(n)]*

and note that it can also be expressed as

*ε = -Ψ(1)*

where *Ψ()* is the digamma function
(Johnson et al., 1992, p.8).

The value of Euler's Constant, to 10 decimal places, is 0.5772156649.

The expression for the mean of a
Type I extreme value (Gumbel) distribution involves Euler's
constant; hence Euler's constant is used to compute the method of moments
estimators for this distribution (see `eevd`

).

Steven P. Millard ([email protected])

Johnson, N. L., S. Kotz, and A.W. Kemp. (1992).
*Univariate Discrete Distributions*. Second Edition.
John Wiley and Sons, New York, pp.4-8.

Johnson, N. L., S. Kotz, and N. Balakrishnan. (1995).
*Continuous Univariate Distributions, Volume 2*.
Second Edition. John Wiley and Sons, New York.

Extreme Value Distribution, `eevd`

.

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