๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Integral representations and asymptotic expansions of the incomplete probability integral

โœ Scribed by P. I. Kuznetsov; A. S. Yudina


Publisher
SP MAIK Nauka/Interperiodica
Year
1972
Tongue
English
Weight
222 KB
Volume
12
Category
Article
ISSN
0001-4346

No coin nor oath required. For personal study only.


๐Ÿ“œ SIMILAR VOLUMES


Integral representations and asymptotic
โœ C. Knessl ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 303 KB

We derive integral representations for the Shannon and Renyi entropies associated with some simple probability distributions. These include the Poisson, binomial, and negative binomial distributions. Then we obtain full asymptotic expansions for the entropies.

Expansions of the exponential integral i
โœ W. Gautschi; F.E. Harris; N.M. Temme ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 289 KB

apparently new expansion of the exponential integral El in incomplete gamma functions is presented and shown to be a limiting csse of a more general expansion given by Mcomi in 1950 without proof. This latter expansion is proved here by interpreting it as a "multiplication theorem". A companion resu

Integral and asymptotic representations
โœ L.B. Klebanov; J.A. Melamed; S. Mittnik; S.T. Rachev ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 179 KB

The fact that geo-stable distributions do not have an explicit representation causes severe difficulties in empirical work. Here, we provide representations for geometric-stable probability densities in terms of fast converging integrals.

Asymptotic expansions of integrals: The
โœ JosรฉL. Lรณpez ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 982 KB

The classical term-by-term integration technique used for obtaining asymptotic expansions of integrals requires the integrand to have an uniform asymptotic expansion in the integration variable. A modification of this method is presented in which the uniformity requirement is substituted by a much w