The Newcomb-Benford Law in its relation to some common distributions

PLoS ONE

Volumn 5, Issue 5, 2010, Pages

  Formann, Anton K ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ACCURACY; ALGORITHM; ARTICLE; CALCULATION; CONTROLLED STUDY; NEWCOMB BENFORD LAW; PROBABILITY; PROCESS OPTIMIZATION; SIMULATION; STATISTICAL ANALYSIS; VALIDITY; HUMAN; NORMAL DISTRIBUTION; THEORETICAL MODEL;

HUMANS; MODELS, THEORETICAL; NORMAL DISTRIBUTION; PROBABILITY;

EID: 77956284542     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0010541     Document Type: Article

References (39)

1. Newcomb S (1881) Note on the frequency of use of the different digits in natural numbers. Am J Math 4: 39-40.
2. Benford F (1938) The law of anomalous numbers. Proc Am Phil Soc 78: 551-572.
3. Raimi RA (1976) The first digit problem. Am Math Mon 83: 521-538.
4. Pinkham RS (1961) On the distribution of first significant digits. Ann Math Stat 32: 1223-1230.
5. Knuth DE (1997) The art of computer programming. Vol.2, 3rd edition. Reading, MA: Addison-Wesley.
6. Furry WH, Hurwitz H (1945) Distribution of numbers and distribution of significant figures. Nature 155: 52-53.
7. Hürlimann W (2006) Benford's law from 1881 to 2006: A bibliography. www.geocities.com/hurlimann53.
8. Berger A, Hill TP (2010) Benford online bibliography. www.benfordonline.net.
9. Hill TP (1995) Base-invariance implies Benford's law. Proc Am Math Soc 123: 887-895.
10. Hill TP (1995) The significant-digit phenomenon. Am Math Mon 102: 322-327.
11. Hill TP (1995) A statistical derivation of the significant-digit law. Stat Sci 10: 354-363.
12. Schatte P (1996) On Benford's law to variable base. Stat Probabil Lett 37: 391-397.
13. Lolbert T (2008) On the non-existence of a general Benford's law. Math Soc Sci 55: 103-106.
14. Irmay S (1997) The relationship between Zipf's law and the distribution of first digits. J Appl Stat 24: 383-393.
15. Luque B, Lacasa L (2009) The first digit frequencies of prime numbers and Riemann zeta zeroes. P Roy Soc A-Math Phy 465: 2197-2216.
16. Miller SJ, Nigrini MJ (2008) Order statistics and Benford's law. arxiv:math/ 0601344v5.
17. Engel H-A, Leuenberger C (2003) Benford's law for exponential random variables. Stat Probabil Lett 63: 361-365.
18. Leemis LM, Schmeiser BW, Evans DL (2000) Survival distributions satisfying Benford's law. Am Stat 54: 236-241.
19. Rodriguez RJ (2004) First significant digit patterns from mixtures of uniform distributions. Am Stat 58: 64-71.
20. Janvresse É, De la Rue T (2004) From uniform distributions to Benford's law. J Appl Probab 41: 1203-1210.
21. Gottwald GA, Nicol M (2002) On the nature of Benford's law. Physica A 303: 387-396.
22. Pietronero L, Tosatti E, Tosatti V, Vespignani A (2001) Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf. Physica A 293: 297-304.
23. Torres J, Fernandez S, Gamero A, Sola A (2007) How do numbers begin? (The first digit law). Eur J Phys 28: L17-L25.
24. Adhikari AK, Sarkar BP (1968) Distribution of most significant digit in certain functions whose arguments are random variables. Sankhya B 30: 47-58.
25. Adhikari AK (1969) Some results on the distribution of most significant digit. Sankhya B 31: 413-420.
26. Dümbgen L, Leuenberger C (2008) Explicit bounds for the approximation error in Benford's law. Elect Comm in Probab 13: 99-112.
27. Ley E (1996) On the peculiar distribution of the US stock indexes' digits. Am Stat 50: 311-313.
28. Hill TP (1998) The first digit phenomenon. Am Sci 86: 358-363.
29. Giles DE (2007) Benford's law and naturally occurring prices in certain ebay auctions. App Econ Lett 14: 157-161.
30. el Sehity T, Hoelzl E, Kirchler E (2005) Price developments after a nominal shock: Benford's law and psychological pricing after the euro introduction. Int J Res Mark 22: 471-480.
31. Nigrini MJ (2000) Digital analysis using Benford's law. Vancouver: Global Audit Publications.
32. Judge G, Schechter L (2009) Detecting problems in survey data using Benford's law. J Hum Resour 44: 1-24.
33. Hales DN, Sridharan V, Radhakrishnan A, Chakravorty SS, Siha SM (2008) Testing the accuracy of employee-reported data: an inexpensive alternative approach to traditional methods. Eur J Oper Res 189: 583-593.
34. Diekmann A (2007) Not the first digit! Using Benford's law to detect fraudulent scientific data. J Appl Stat 34: 321-329.
35. Browne MW (1998) Following Benford's law, or looking out for no. 1. The New York Times, August 4, 1998.
36. Beer TW (2009) Terminal digit preference: beware of Benford's law. J Clin Pathol 62: 192.
37. Kim H-J (2006) On the ratio of two folded normal distributions. Commun Stat- Theor M 35: 965-977.
38. Hinkley DV (1969) On the ratio of two correlated normal random variables. Biometrika 56: 635-639.
39. Johnson NL, Kotz S, Balakrishnan N (1994) Continuous univariate distributions - Vol 1. New York: Wiley.