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Journal Article

Distribution of Most Significant Digit in Certain Functions Whose Arguments Are Random Variables

A. K. Adhikari and B. P. Sarkar
Sankhyā: The Indian Journal of Statistics, Series B (1960-2002)
Vol. 30, No. 1/2 (Jun., 1968), pp. 47-58
Stable URL: http://www.jstor.org/stable/25051623
Page Count: 12

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Topics: Random variables, Random numbers, Integers
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Distribution of Most Significant Digit in Certain Functions Whose Arguments Are Random Variables
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Abstract

It is empirically well established that in large collections of numbers the proportions of entries with the most significant digit A is ${\rm log}_{10}$ (A+1)/A. The property of the most significant digit has been studied in the present paper. It has been proved that when random numbers or their reciprocals are raised to higher and higher powers, they have log distribution of most significant digit in the limit. The property is also demonstrated in the limit by the products of random numbers as the number of terms in the product becomes higher and higher. The property is not, however, demonstrated by higher roots of the random numbers or their reciprocals in the limit. In fact there is a concentration at some particular digit. It has been shown that if X has log distribution of the most significant digit, so does 1/X and CX, C being any constant, under stronger conditions.

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