Letting P(u,x) denote the regularised incomplete gamma function, it is shown that for each α ≥ 0, P(x,x+α) decreases as x increases on the positive real semi-axis, and P(x,x+α) converges to 1/2 as x tends to infinity. The statistical significance of these results is explored.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-3-7,
author = {Wojciech Chojnacki},
title = {Some monotonicity and limit results for the regularised incomplete gamma function},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {283-291},
zbl = {1157.33302},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-3-7}
}
Wojciech Chojnacki. Some monotonicity and limit results for the regularised incomplete gamma function. Annales Polonici Mathematici, Tome 93 (2008) pp. 283-291. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-3-7/