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Volumn 10, Issue 4, 1995, Pages 354-363

A statistical derivation of the significant-digit law

Author keywords

Base invariance; Benford s law; First digit law; Logarithmic law; Mantissa; Mantissa sigma algebra; Random distributions; Random k samples; Random probability measures; Scale invariance; Significant digit law

Indexed keywords


EID: 84972541029     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/ss/1177009869     Document Type: Article
Times cited : (424)

References (33)
  • 1
    • 0008117113 scopus 로고
    • Distribution of most significant digit in certain functions whose arguments are random variables
    • ADHIKARI, A. and SARKAR, B. (1968). Distribution of most significant digit in certain functions whose arguments are random variables. Sankhya Ser. B 30 47-58.
    • (1968) Sankhya Ser. B , vol.30 , pp. 47-58
    • Adhikari, A.1    Sarkar, B.2
  • 2
    • 0021977936 scopus 로고
    • On roundoff error distributions in floating point and logarithmic arithmetic
    • BARLOW, J. and BAREISS, E. (1985). On roundoff error distributions in floating point and logarithmic arithmetic. Computing 34 325-347.
    • (1985) Computing , vol.34 , pp. 325-347
    • Barlow, J.1    Bareiss, E.2
  • 3
    • 0020139872 scopus 로고
    • Patterns in listings of failure-rate and MTTF values and listings of other data
    • BECKER, P. (1982). Patterns in listings of failure-rate and MTTF values and listings of other data. IEEE Transactions on Reliability R-31 132-134.
    • (1982) IEEE Transactions on Reliability , vol.R-31 , pp. 132-134
    • Becker, P.1
  • 5
    • 1842707242 scopus 로고
    • He’s got their number: Scholar uses math to foil financial fraud
    • July 10
    • BERTON, L. (1995). He’s got their number: scholar uses math to foil financial fraud. Wall Street Journal, July 10.
    • (1995) Wall Street Journal
    • Berton, L.1
  • 6
    • 0038695506 scopus 로고
    • An illustration of Benford’s first digit law using alpha decay half lives
    • BUCK, B., MERCHANT, A. and PEREZ, S. (1993). An illustration of Benford’s first digit law using alpha decay half lives. European J. Phys. 14 59-63.
    • (1993) European J. Phys , vol.14 , pp. 59-63
    • Buck, B.1    Merchant, A.2    Perez, S.3
  • 7
    • 34247875563 scopus 로고
    • Benford’s law and physical constants: The distribution of initial digits
    • BURKE, J. and KINCANON, E. (1991). Benford’s law and physical constants: the distribution of initial digits. Amer. J. Phys. 59 952.
    • (1991) Amer. J. Phys , vol.59 , pp. 952
    • Burke, J.1    Kincanon, E.2
  • 8
    • 33847293440 scopus 로고
    • An explanation of the first digit phenomenon
    • COHEN, D. (1976). An explanation of the first digit phenomenon. J. Combin. Theory Ser. A 20 367-370.
    • (1976) J. Combin. Theory Ser. A , vol.20 , pp. 367-370
    • Cohen, D.1
  • 9
    • 48549113518 scopus 로고
    • Prime numbers and the first digit phenomenon
    • COHEN, D. and KATZ, T. (1984). Prime numbers and the first digit phenomenon. J. Number Theory 18 261-268.
    • (1984) J. Number Theory , vol.18 , pp. 261-268
    • Cohen, D.1    Katz, T.2
  • 11
    • 0002417821 scopus 로고
    • The distribution of leading digits and uniform distribution mod 1
    • DIACONIS, P. (1977). The distribution of leading digits and uniform distribution mod 1. Ann. Probab. 5 72-81.
    • (1977) Ann. Probab , vol.5 , pp. 72-81
    • Diaconis, P.1
  • 14
    • 0001590086 scopus 로고
    • Overflow, underflow, and severe loss of significance in floating-point addition and subtraction
    • FELDSTEIN, A. and TURNER, P. (1986). Overflow, underflow, and severe loss of significance in floating-point addition and subtraction. IMA J. Numer. Anal. 6 241-251.
    • (1986) IMA J. Numer. Anal , vol.6 , pp. 241-251
    • Feldstein, A.1    Turner, P.2
  • 15
    • 0000030933 scopus 로고
    • On the probability that a random number has initial digit A
    • FLEHINGER, B. (1966). On the probability that a random number has initial digit A. Amer. Math. Monthly 73 1056-1061.
    • (1966) Amer. Math. Monthly , vol.73 , pp. 1056-1061
    • Flehinger, B.1
  • 16
    • 0014855186 scopus 로고
    • On the distribution of numbers
    • HAMMING, R. (1970). On the distribution of numbers. Bell System Technical Journal 49 1609-1625.
    • (1970) Bell System Technical Journal , vol.49 , pp. 1609-1625
    • Hamming, R.1
  • 17
    • 84966250122 scopus 로고
    • Base-invariance implies Benford’s law
    • HILL, T. (1995a). Base-invariance implies Benford’s law. Proc. Amer. Math. Soc. 123 887-895.
    • (1995) Proc. Amer. Math. Soc , vol.123 , pp. 887-895
    • Hill, T.1
  • 18
    • 21844487115 scopus 로고
    • The significant-digit phenomenon
    • HILL, T. (1995b). The significant-digit phenomenon. Amer. Math. Monthly 102 322-327.
    • (1995) Amer. Math. Monthly , vol.102 , pp. 322-327
    • Hill, T.1
  • 19
    • 44049110407 scopus 로고
    • The logarithmic distribution of leading digits and finitely additive measures
    • JECH, T. (1992). The logarithmic distribution of leading digits and finitely additive measures. Discrete Math. 108 53-57.
    • (1992) Discrete Math , vol.108 , pp. 53-57
    • Jech, T.1
  • 22
    • 84972540812 scopus 로고
    • On the peculiar distribution of the U.S. stock indices digits
    • To appear
    • LEY, E. (1995). On the peculiar distribution of the U.S. stock indices digits. Amer. Statist. To appear.
    • (1995) Amer. Statist
    • Ley, E.1
  • 23
    • 84969882200 scopus 로고
    • 4th ed. Springer, New York
    • LOEVE, M. (1977). Probability Theory 1, 4th ed. Springer, New York.
    • (1977) Probability Theory , pp. 1
    • Loeve, M.1
  • 24
    • 0003038640 scopus 로고
    • Note on the frequency of use of the different digits in natural numbers
    • NEWCOMB, S. (1881). Note on the frequency of use of the different digits in natural numbers. Amer. J. Math. 4 39-40.
    • (1881) Amer. J. Math , vol.4 , pp. 39-40
    • Newcomb, S.1
  • 25
    • 84972501012 scopus 로고
    • Private communication
    • NIGRINI, M. (1995). Private communication.
    • (1995)
    • Nigrini, M.1
  • 28
    • 0001025497 scopus 로고
    • The peculiar distribution of first digits
    • December
    • RAIMI, R. (1969). The peculiar distribution of first digits. Scientific American December 109-119.
    • (1969) Scientific American , pp. 109-119
    • Raimi, R.1
  • 29
    • 0037611243 scopus 로고
    • The first digit problem
    • RAIMI, R. (1976). The first digit problem. Amer. Math. Monthly 102 322-327.
    • (1976) Amer. Math. Monthly , vol.102 , pp. 322-327
    • Raimi, R.1
  • 31
    • 0010075497 scopus 로고
    • On mantissa distributions in computing and Benford’s law
    • SCHATTE, P. (1988). On mantissa distributions in computing and Benford’s law. J. Inform. Process. Cybernet. 24 443-455.
    • (1988) J. Inform. Process. Cybernet , vol.24 , pp. 443-455
    • Schatte, P.1
  • 32
    • 0038019128 scopus 로고
    • Benford’s law
    • VARIAN, H. (1972). Benford’s law. Amer. Statist. 23 65-66.
    • (1972) Amer. Statist , vol.23 , pp. 65-66
    • Varian, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.