Contribution to the history of laplacian tests

Abstract

-Au croisement des recherches historiques de Bernard Bru sur la statistique laplacienne, et des interrogations récurrentes depuis les années 1960 sur les usages peu satisfaisants des tests statistiques dans les sciences d'observation, nous revisitons la mise en place des tests statistiques dans l'oeuvre de Laplace. On trouve déjà dans celle-ci un mélange entre plusieurs approches, et des audaces interprétatives, dignes de la version aujourd'hui pratiquée, hybride entre les apports de Bayes-Laplace, Fisher et Neyman.

Study of Households' Income in Poland by Using the Statistical Physics Approach

“…The fact that the cumulative log-normal distribution shows a good agreement with empirical data result directly from Rules of Proportionate Growth. In this model was assumed that changes in income are small, which is indeed justified in the case of poor households [9]. In turn, the weak law of Pareto is appropriate to depict income of middle households.…”

“…We also fitted the cumulative log-normal distribution resulting from rules of proportionate growth [9]:…”

Modelling of income distribution in the European Union with the Fokker–Planck equation

“…This type of stochastic process is called the multiplicative stochastic process. Hence, coefficients A(m) and B(m) obey the proportionality principle of Gibrat [10,11]:…”

“…Pareto's economic discoveries initiated attempts of analytical descriptions of incomes of the societies and inspired an avalanche of related research works [2,3,[5][6][7][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Among them, particularly significant are those of the economist Robert Gibrat [7,10,11].…”

“…Among them, particularly significant are those of the economist Robert Gibrat [7,10,11]. He found that the complementary cumulative distribution function of the Pareto distribution is insufficient to describe empirical data within the whole range of the income.…”