Sankhya-The Indian Journal of Statistics Series B, 31 (Dec), pp. 413-420.
ISSN/ISBN: 0581-5738 DOI: Not available at this time.
Abstract: This paper finds the distribution of the most significant digit of some functions of random variables X_{1}, X_{2}, … , X_{n}, where these variables are independent and distributed uniformly in (0, 1). The probability that the most significant digit of Y_{n} is A (A=1, … , 9) has been found, where Y_{n} is defined as the products of the reciprocals of n such random variables. It has been shown that this probability tends to log_{10}(A+1)/A as n tends to infinity. Similarly if Z_{n} is defined as Z_{n}=X_{1}/X_{2}/… /X_{n+1}, it has been proved that the probability distribution of the most significant digit of Z_{n} also tends to log_{10}(A+1)/A as n tends to infinity. More generally, it is found that if V_{1}, V_{2}, … , V_{n} are defined as V_{1}=B/X, … , V_{n}=V_{n-1}/X_{n} where B is any random variable defined on the positive axis of the real line, the probability distribution of the most significant digit tends to log_{10}(A+1)/A as n tends to infinity.
Bibtex:
@article {,
AUTHOR = {Adhikari, A. K.},
TITLE = {Some results on the distribution of the most significant
digit},
JOURNAL = {Sankhy\=a Ser. B},
FJOURNAL = {Sankhy\=a (Statistics). The Indian Journal of Statistics.
Series B},
VOLUME = {31},
YEAR = {1969},
PAGES = {413--420},
ISSN = {0581-5738},
MRCLASS = {62.10},
MRNUMBER = {0279920 (43 \#5641)},
}
Reference Type: Journal Article
Subject Area(s): Probability Theory