Fixed point properties of the binomial function

✍ Scribed by Douglas N. Green

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 594 KB
• Volume: 316
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(83)90029-7

✦ Synopsis

Fixed point properties of the binomial function N N T#P) i C 0 p"(1 -py-" n=L n are deoeloped. It is shown thatjtir any 1 < L < N, Tk has a uniquefixed point p in (0, l), and that ,for large N, thejixed point is L/N. This has application to signal detection schemes commonly used in communication systems. When detecting the presence or absence of a signal with an initial ,false alarm probability pFA and an initial detection probability pD, then Tk(pFA) < pFA and Tk(p,) > pD iL and only l$ pFa < p < pD When this condition is satisfied, as N + CL, T,~(PF~ + 0 and TV; + 1.