| Title:
|
On properties of binary random numbers (English) |
| Author:
|
Víšek, Jan Ámos |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
19 |
| Issue:
|
6 |
| Year:
|
1974 |
| Pages:
|
375-385 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\{X_k\}^\infty_{k=1}$ be a sequence of independent zero-one random variables (rv) with $P(X_k=1)=\frac{1}{2} + \Delta$. Then we define the binary random number (brn) $Y=\sum^\infty_{k=1} X_k2^{-k}$. An ideal generator produces 0 and 1 with equal probability, but a real one does it only approximately. The purpose of this paper is to find distribution of brn for $-\frac{1}{2}<\Delta <\frac{1}{2}$ (also $\Delta =\Delta_k$). Particularly, convergence of the normed sum of brn to normally distributed rv is studied by means of Edgeworth expansion. () |
| MSC:
|
60F05 |
| MSC:
|
60F99 |
| MSC:
|
65C10 |
| idZBL:
|
Zbl 0303.60020 |
| idMR:
|
MR0375442 |
| DOI:
|
10.21136/AM.1974.103555 |
| . |
| Date available:
|
2008-05-20T18:00:00Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103555 |
| . |
| Reference:
|
[1] Г. А. Козлов: О распределении случайных чисел, вырабатываемых последовательными физическими датчиками.Теория вероятностней 16 (1971) 370. Zbl 1168.35423 |
| Reference:
|
[2] M. Kаc: Statistical Independence in Probability Analysis and Number Theory.Carus Mathematical Monograph, No. 12 The Mathematical Association of America, 1959. MR 0110114 |
| Reference:
|
[3] Jessen-Wintner: Distributions and the Riemann Zeta functions.Trans. Amer. Math. Soc. 38, 48-88 (1935). MR 1501802, 10.1090/S0002-9947-1935-1501802-5 |
| Reference:
|
[4] В. В. Петров: Суммы независимых случайных величин.Москва 1972. Zbl 1156.34335 |
| . |
