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Adhikari, AK (1969)

Some Results on Distribution of Most Significant Digit

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