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The exponential integral distribution. (English) Zbl 0615.60013
For a positive integer n let $E\sb n\sp{(0)}(x)=\exp (-x)$ and $$ E\sb n\sp{(m+1)}(x)=x\sp{n-1}\int\sp{\infty}\sb{x}E\sb n\sp{(m)}(t)t\sp{- n}dt\quad for\quad m=0,1,2,.... $$ The exponential integral distribution with parameters m, n and $\nu$ $(>0)$ is then described by the probability density function $$ f(x)=(n+\nu -1)\sp mx\sp{\nu -1}E\sb n\sp{(m)}(x)/\Gamma (\nu),\quad for\quad x>0. $$ Expressions for the moments and the cumulative distribution function are given and physical relevance of this distribution is discussed. With $m=0$, this reduces to a gamma distribution.
Reviewer: H.N.Nagaraja

60E05General theory of probability distributions
33B15Gamma, beta and polygamma functions
33E99Other special functions
Full Text: DOI
[1] Feller, W.: An introduction to probability theory and its applications. 2 (1971) · Zbl 0219.60003
[2] Abramowitz, M.; Stegun, I. A.: Handbook of mathematical functions. (1970) · Zbl 0171.38503
[3] Van De, H. C. Hulst: Multiple light scattering. 1 (1980)
[4] Milgram, M. S.: The generalized integro-exponential function. Math. of computation 44, 443-458 (1985) · Zbl 0593.33001
[5] Lewin, L.: Polylogarithms and associated functions. (1981) · Zbl 0465.33001
[6] Gilbert, E. N.; Pollak, H. O.: Amplitude distribution of shot noise. Bell system technical journal 39, 333-350 (1960)