I think I did understand the definition of the Lorenz curve (as a check on this I got the same answer to the example you cite; it is my case 4b).

But I don’t yet understand why my statement which you quoted is not true. I need to think about that, since as you imply it may help get me unstuck.

After you have found this command in comments.php you should be able to write what ever you want after it.

unless you dont get problems with the latex commands.

in the middle section you see then the contents of comments.php somewhere in the test there should be a
Leave a Reply

typo: ..somewhere in the text there should be…

I am not sure wether its clear for you what my comments above were about.

the text in the middle (i.e. the content of the file comments.php) is written in (PHP) and I tried to write down the command
h3 id=”respond”>Leave a Reply</h3
(in comments.php it should have brackets around) which
you should look for but this expression
was executed by wordpress, despite several attempts to escape this.

After you have found this command in comments.php you should be able to write what ever you want after it.

The Lorenz curve is the integral of the inverse of the integral of the probability distribution of income (OK, normalized to make it a percentage).

No, that’s not true: it’s simpler than that. This is why you got stuck. The Lorenz curve shows for the bottom x% of households, what percentage y% of the total income they have. So, for example, if everyone has the same income the Lorenz curve is a diagonal straight line, as shown here:

The case where everyone has the same income is a bit degenerate, but in this case “the bottom x% of households” just means “any x% of households”. Everyone is at the bottom and everyone is at the top, in this case!

1) The Lorenz curve is the integral of the inverse of the integral of the probability distribution of income (OK, normalized to make it a percentage).
2) So one restatement is: When you majorize a probability distribution (roughly, when you make it “less flat”), what happens to the normalized integral of the inverse of its integral?
3) I have no clue.
4) OK let’s try a few:
a. The Lorenz curve La of the uniform distribution (N equally populated income brackets, assume equally spaced) approximates a parabola.
b. The Lorenz curve Lb of a “spike” distribution (all incomes identical) is a diagonal line which lies above La.
c. The Lorenz curve Lc of a “half-impoverished-half-rich” distribution crosses La.
d. There are also distributions whose Lorenz curves lie on-or-below La.

Hmm. Distributions b-d all majorize a; but their Lorenz curves are all over the map (at least, in the respects I’m considering) relative to a’s.

..So I got nothing. Would one of you do the humane thing and post a solution? Quickly please, this is getting ugly.