Gibrat's law

Japanese: ジブラ法則 - ジブラほうそく（英語表記）Gibrat's law

This is one of the laws for measuring the distribution of income, wealth, etc., and was proposed by the French statistician R. Gibrat in 1931. It states that income distribution follows a log-normal distribution and is expressed as the following equation.
y is the number of people, x is the amount _of income, x0 is the adjustment value (usually the minimum income), and a is called the Gibrat coefficient; the larger a is, the less unequal the income distribution is. Similarly, the Pareto coefficient is used to represent income distribution, but this coefficient does not fit well, and is not particularly effective for high-income and low-income groups. The Gibrat coefficient corrects this shortcoming, and is an index that is economically meaningful and statistically easy to manipulate. It is used not only to measure income distribution, but also to measure the degree of inequality in the distribution of various economic quantities that generally follow a log-normal distribution, such as wages and the number of companies.

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:

所得，富などの分布を計測する法則の一つで，フランスの統計学者 R.ジブラが 1931年に提案した。その内容は所得分布が対数正規分布に従うというもので，次式で表わされる。
y は人員，x は所得金額，x₀ は修正値 (通常は最低所得) で，a をジブラ係数と呼び，a が大きいほど所得分布の不平等度は小さい。同様に所得分布を表わすものにパレート係数があるが，この係数は適合度があまりよくなく，特に高所得層，低所得層に対しては有効でないのに対し，ジブラ係数はこの欠点を正し，かつ経済学的に意味があり，統計学的にも操作の容易な指数である。所得分布だけでなく，一般に対数正規分布をする種々の経済量，たとえば賃金，企業数などの分布の不均等度の測定にも用いられる。

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