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Tests d'adéquation à la loi de Newcomb-Benford comme outils de détection de fraudes

Abstract : I propose to you the following bet: let us open the newspaper, choose a random page, and note the first number which we see. If the first significant figure of this number is higher than 3, I will give you 100 euros, if not you will give me 100 euros. It seems to you that the proposal is clearly favorable to you: there are indeed only three numbers that make me win (1,2,3), while there are six for you (4,5,6,7,8,9); the 0 does not count, because it cannot be a first significant number. So, you think you'll win twice out of three times. Would I be a fool to offer you such a bet ? Well, no: if you accept, I will win more than 60 percent of the time. Surprisingly, the first significant digit of a number you see in a newspaper article is not as likely to be a 1, a 2, a 3, ..., or a 9(the probability would be 1/9, or 11.11 percent). The Newcomb-Benford law indicates that, in a general context like a newspaper article ones, the probabilities “p” in percent of encountering the various digits as the first significant digit are: p(1)=30.1; p(2)=17.6; p(3)=12.5; p(4)=9.7; p(5)=7.9; p(6)=6.7; p(7)=5.8; p(8)=5.1; and p(9)=4.6 . Since 30.1+17.6+2.5=60.2, I will win my bet 60.2 percent of the time. How to test the quality of the adjustment of the data to this law which is so contrary to the intuition?Wong (2010) provided answers to this question using the first and second significant figures based on the work of Lesperance et al. (2016) on the first significant figure. On the other hand, Cerioli et al. (2018) provides motivation for new tests of compliance with Newcomb-Benford law. The goal of this work is therefore to propose new adequate tests based on the smooth tests of Neyman (1937). We study the power of our tests under different alternatives, and we concluded that our test is globally preferable to existing ones.
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Komlavi Vovor-Dassu. Tests d'adéquation à la loi de Newcomb-Benford comme outils de détection de fraudes. Statistiques [math.ST]. Université Montpellier, 2021. Français. ⟨NNT : 2021MONTS086⟩. ⟨tel-03595714⟩

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