Gini Coefficient Calculator in R

How To Calculate Gini Coefficient In R

Gini Coefficient Formula:

\[ G = \frac{\sum_{i=1}^n \sum_{j=1}^n |x_i - x_j|}{2n^2\bar{x}} \]

Gini Coefficient:

R Code:

library(ineq)
data <- c()
gini_index <- Gini(data)
print(gini_index)

1. What is the Gini Coefficient?

The Gini coefficient is a measure of statistical dispersion intended to represent income or wealth distribution of a nation's residents. It ranges from 0 (perfect equality) to 1 (perfect inequality).

2. How Does the Calculator Work?

The calculator uses the ineq package in R to compute the Gini coefficient:

\[ G = \frac{\sum_{i=1}^n \sum_{j=1}^n |x_i - x_j|}{2n^2\bar{x}} \]

Where:

\( x_i, x_j \) — Individual values in the dataset
\( n \) — Number of observations
\( \bar{x} \) — Mean of all values

Explanation: The Gini coefficient measures the average difference between all pairs of values, normalized by the mean.

3. Interpretation of Results

Details:

0 = Perfect equality (everyone has the same income)
0.2-0.3 = Relatively equal distribution
0.4-0.5 = High inequality
1 = Perfect inequality (one person has all income)

4. Using the Calculator

Tips: Enter numeric values separated by commas. The calculator will process them in R using the Gini() function from the ineq package.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Gini and other inequality measures?
A: Gini is more sensitive to changes in the middle of the distribution compared to measures like the 90/10 ratio.

Q2: What are typical Gini values for countries?
A: Scandinavian countries typically have values around 0.25, while highly unequal societies may exceed 0.5.

Q3: Can Gini be greater than 1?
A: Normally no, but with negative values in the dataset, it's theoretically possible (though economically meaningless).

Q4: What are limitations of the Gini coefficient?
A: It doesn't show where inequality occurs in the distribution and can be sensitive to outliers.

Q5: How is Gini related to the Lorenz curve?
A: Gini is the ratio of the area between the Lorenz curve and the line of equality to the total area under the line of equality.