Gini coefficient

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Hi I’m learning about inequality measures, there are several ways to calculate it and i understand all but 1.



$kappa = frac2E(X)$



I’m not sure what the second x means in the case of random variables.



Thanks for your help






gini







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  • 1




    Put $kappa = frac2E(X)$ to get $kappa = frac2E(X)$.... MathJax quick reference: math.meta.stackexchange.com/questions/5020/…
    – Glen_b♦
    4 hours ago











  • Thanks I edited my post
    – Petra
    16 mins ago
















up vote
1
down vote

favorite












Hi I’m learning about inequality measures, there are several ways to calculate it and i understand all but 1.



$kappa = frac2E(X)$



I’m not sure what the second x means in the case of random variables.



Thanks for your help






gini







share|cite|improve this question



















  • 1




    Put $kappa = frac2E(X)$ to get $kappa = frac2E(X)$.... MathJax quick reference: math.meta.stackexchange.com/questions/5020/…
    – Glen_b♦
    4 hours ago











  • Thanks I edited my post
    – Petra
    16 mins ago












up vote
1
down vote

favorite









up vote
1
down vote

favorite











Hi I’m learning about inequality measures, there are several ways to calculate it and i understand all but 1.



$kappa = frac2E(X)$



I’m not sure what the second x means in the case of random variables.



Thanks for your help






gini







share|cite|improve this question















Hi I’m learning about inequality measures, there are several ways to calculate it and i understand all but 1.



$kappa = frac2E(X)$



I’m not sure what the second x means in the case of random variables.



Thanks for your help






gini




gini






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 17 mins ago

























asked 5 hours ago









Petra

555




555







  • 1




    Put $kappa = frac2E(X)$ to get $kappa = frac2E(X)$.... MathJax quick reference: math.meta.stackexchange.com/questions/5020/…
    – Glen_b♦
    4 hours ago











  • Thanks I edited my post
    – Petra
    16 mins ago












  • 1




    Put $kappa = frac2E(X)$ to get $kappa = frac2E(X)$.... MathJax quick reference: math.meta.stackexchange.com/questions/5020/…
    – Glen_b♦
    4 hours ago











  • Thanks I edited my post
    – Petra
    16 mins ago







1




1




Put $kappa = frac2E(X)$ to get $kappa = frac2E(X)$.... MathJax quick reference: math.meta.stackexchange.com/questions/5020/…
– Glen_b♦
4 hours ago





Put $kappa = frac2E(X)$ to get $kappa = frac2E(X)$.... MathJax quick reference: math.meta.stackexchange.com/questions/5020/…
– Glen_b♦
4 hours ago













Thanks I edited my post
– Petra
16 mins ago




Thanks I edited my post
– Petra
16 mins ago










1 Answer
1






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3
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The numerator of the Gini index is the expected value of the difference, in absolute value, between the earnings (if $x$ denotes earnings) of two random individuals in the population.



In mathematical terms, the expectation here is taken over two random variables $x$ and $x'$, taken as independent and identically distributed. If I rewrite the Gini with $x_1$ and $x_2$ for convenience, and if $F(.)$ denotes the cdf of these random variables:
$$
G = frac1E(X)int int |x_1 - x_2| dF(x_1) dF(x_2),
$$
where:
$$
E(X) = int x dF(x).
$$



You could find more information on the Wikipedia page of the Gini index.






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  • 1




    See also, quite independently of income inequality and so forth, the ideas of $L$-moments.
    – Nick Cox
    4 hours ago










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1 Answer
1






active

oldest

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1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
3
down vote













The numerator of the Gini index is the expected value of the difference, in absolute value, between the earnings (if $x$ denotes earnings) of two random individuals in the population.



In mathematical terms, the expectation here is taken over two random variables $x$ and $x'$, taken as independent and identically distributed. If I rewrite the Gini with $x_1$ and $x_2$ for convenience, and if $F(.)$ denotes the cdf of these random variables:
$$
G = frac1E(X)int int |x_1 - x_2| dF(x_1) dF(x_2),
$$
where:
$$
E(X) = int x dF(x).
$$



You could find more information on the Wikipedia page of the Gini index.






share|cite|improve this answer


















  • 1




    See also, quite independently of income inequality and so forth, the ideas of $L$-moments.
    – Nick Cox
    4 hours ago














up vote
3
down vote













The numerator of the Gini index is the expected value of the difference, in absolute value, between the earnings (if $x$ denotes earnings) of two random individuals in the population.



In mathematical terms, the expectation here is taken over two random variables $x$ and $x'$, taken as independent and identically distributed. If I rewrite the Gini with $x_1$ and $x_2$ for convenience, and if $F(.)$ denotes the cdf of these random variables:
$$
G = frac1E(X)int int |x_1 - x_2| dF(x_1) dF(x_2),
$$
where:
$$
E(X) = int x dF(x).
$$



You could find more information on the Wikipedia page of the Gini index.






share|cite|improve this answer


















  • 1




    See also, quite independently of income inequality and so forth, the ideas of $L$-moments.
    – Nick Cox
    4 hours ago












up vote
3
down vote










up vote
3
down vote









The numerator of the Gini index is the expected value of the difference, in absolute value, between the earnings (if $x$ denotes earnings) of two random individuals in the population.



In mathematical terms, the expectation here is taken over two random variables $x$ and $x'$, taken as independent and identically distributed. If I rewrite the Gini with $x_1$ and $x_2$ for convenience, and if $F(.)$ denotes the cdf of these random variables:
$$
G = frac1E(X)int int |x_1 - x_2| dF(x_1) dF(x_2),
$$
where:
$$
E(X) = int x dF(x).
$$



You could find more information on the Wikipedia page of the Gini index.






share|cite|improve this answer














The numerator of the Gini index is the expected value of the difference, in absolute value, between the earnings (if $x$ denotes earnings) of two random individuals in the population.



In mathematical terms, the expectation here is taken over two random variables $x$ and $x'$, taken as independent and identically distributed. If I rewrite the Gini with $x_1$ and $x_2$ for convenience, and if $F(.)$ denotes the cdf of these random variables:
$$
G = frac1E(X)int int |x_1 - x_2| dF(x_1) dF(x_2),
$$
where:
$$
E(X) = int x dF(x).
$$



You could find more information on the Wikipedia page of the Gini index.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited 4 hours ago

























answered 5 hours ago









Roland

38115




38115







  • 1




    See also, quite independently of income inequality and so forth, the ideas of $L$-moments.
    – Nick Cox
    4 hours ago












  • 1




    See also, quite independently of income inequality and so forth, the ideas of $L$-moments.
    – Nick Cox
    4 hours ago







1




1




See also, quite independently of income inequality and so forth, the ideas of $L$-moments.
– Nick Cox
4 hours ago




See also, quite independently of income inequality and so forth, the ideas of $L$-moments.
– Nick Cox
4 hours ago

















 

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