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 X1, X2, … , Xn, where these variables are independent and distributed uniformly in (0, 1). The probability that the most significant digit of Yn is A (A=1, … , 9) has been found, where Yn is defined as the products of the reciprocals of n such random variables. It has been shown that this probability tends to log10(A+1)/A as n tends to infinity. Similarly if Zn is defined as Zn=X1/X2/… /Xn+1, it has been proved that the probability distribution of the most significant digit of Zn also tends to log10(A+1)/A as n tends to infinity. More generally, it is found that if V1, V2, … , Vn are defined as V1=B/X, … , Vn=Vn-1/Xn 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 log10(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