Some monotonicity and limit results for the regularised incomplete gamma function

Volume 94 / 2008

Wojciech Chojnacki Annales Polonici Mathematici 94 (2008), 283-291 MSC: Primary 33B15; Secondary 62H12. DOI: 10.4064/ap94-3-7


Letting $P(u,x)$ denote the regularised incomplete gamma function, it is shown that for each $\alpha \geq 0$, $P(x,x+\alpha )$ decreases as $x$ increases on the positive real semi-axis, and $P(x,x+\alpha )$ converges to $1/2$ as $x$ tends to infinity. The statistical significance of these results is explored.


  • Wojciech ChojnackiSchool of Computer Science
    The University of Adelaide
    Adelaide, SA 5005, Australia
    Wydzia/l Matematyczno-Przyrodniczy
    Szko/la Nauk Ścis/lych
    Uniwersytet Kardyna/la Stefana Wyszyńskiego
    Dewajtis 5, 01-815 Warszawa, Poland

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