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I agree, I had trouble learning about the Lorenz curve from this page because the cdf is different. The cdf plots the cumulative % of the variable against the category. The Lorenz plots the cumulative % of the variable against the cumulative % of population (calculated from the categories). The first sentence and the graph labeling should be revised. —Preceding unsigned comment added by Intlthahc ( talk • contribs) 20:37, 12 January 2008 (UTC)
Is it really a "cumulative" dist. fn. ?? The the y-axis gives the sum as a PERCENTAGE of the total, whereas in the cdf, the y-axis will give the un-normalized sum. This will produce a logrithmic-shaped graph rather than an exponential one... Nigel, May 7, 2006
Nigel, after sorting individuals from poorest to richest, the point (x,y), tells us the cumulative number of individuals (on the x-axis) and the cumulative wealth of those individuals (y-axis). A cumulative distribution function would put wealth (not cumulative) on the x-axis and number of people (cumulative) on the y-axis.
Polymer scientists approach the distribution of polymer molecular weights in a polymer samples (same concept as distribution of wealth among individuals) in yet another way. We talk about number distributions and weight distributions (neither one cumulative), often use logarithmic scales for the molecular weight, and use the ratio of the weight average molecular weight to the number average as a measure of dispersity. I would not be surprised to hear of other fields that treat mathematically equivalent problems in still other ways. I suspect that "least confusing" depends on precisely what one's question is and/or what one is already familiar with -- Emil M Friedman — Preceding unsigned comment added by Emilfriedman ( talk • contribs) 18:11, 23 September 2014 (UTC)
The curve is apparently always convex. Is there any corner case that it's not convex? — Preceding unsigned comment added by 74.117.104.162 ( talk) 12:30, 23 October 2019 (UTC)
If the variable being measured can take negative values but has a positive mean, then the Lorenz curve will sink below the line of perfect inequality and is a convex function.
If the variable being measured can take negative values and has a negative mean, then the Lorenz curve will be above the line of perfect equality, except at the end points, and is a concave function.
^ I've edited this out. This convex statement is BS. It can easily be non convex and still be monotonic increasing. The graph pictured is misleading. Jasmine85 ( talk) 10:07, 3 September 2009 (UTC)
The Lorenz curve is convexe and not concave as is said in the text, see the graph below.
Can we get a real life example for the illustration from some place? Paranoid 20:10, 6 Jan 2005 (UTC)
The Lorenz Curve is used in geography as well to represent unequal distribution of the world's population over area...please add that in
'... we call this line the line of perfect equality or the 45° line.' It's only 45° when both axes have equal scales.
Holy Cow 20:55, 18 March 2006 (UTC)
What does a Lorenz curve look like for a discrete probability function? What are the formulas for calculating the curve in such a case? DCary 04:19, 26 May 2006 (UTC)
Is x(F), the inverse of F(x), equal F-1(f(x))? -- Kwj2772 ( talk) 13:21, 17 July 2009 (UTC)
The article waffles back and forth on whether this curve typically represents income or wealth, which are completely distinct measures. Which one is kind of important. -- 75.94.164.123 ( talk) 14:11, 28 June 2011 (UTC)
would like an explanation (it may have been buried in the math, didn't look) as to why the curve cannot hump above the perfect equality line when non-negative variables are used. It would seem that a decreasing increase is possible. — Preceding unsigned comment added by Barnsward ( talk • contribs) 19:42, 15 August 2011 (UTC) never mind, i see that if all are lined up in ascending order on the x axis there has to be an increasing increase. — Preceding unsigned comment added by 69.123.186.12 ( talk) 23:17, 15 August 2011 (UTC)
Is there a proof of the below, can some one add citation, or simply prove it.
In "Definition and calculation" section: Please define Fi, Si, and Li; or at least F, S, and L. I couldn't find any "...where S equals..." Thank you 71.139.166.86 ( talk) 23:12, 22 February 2014 (UTC)
I think the image found here is very helpful. It shouldn't be difficult for someone with basic skills in graph making (which I lack) to recreate it in a free version. -- Piotr Konieczny aka Prokonsul Piotrus| reply here 09:08, 29 April 2014 (UTC)
The real world sample graphic isn't showing Denmark at all, contrary to its caption. Lewis Goudy ( talk) 16:00, 25 March 2017 (UTC)
In the case of perfectly equal wealth distribution, why is the lorenz curve considered to be a straight line? For example, in that case, how would you decided which 10% of the population is the "bottom" 10% ? As a mathematical technicality, don't we have to assume that individuals with equal wealth will be ranked in some arbitrary order?
Tashiro~enwiki ( talk) 15:34, 9 October 2016 (UTC)
The independent variable is not the set of individuals but rather the size of that set as a fraction of the size of the total population. We are modeling a discrete situation using continuous mathematics, so we represent the cumulative presentation as a piecewise linear function rather than a step function. In the equal wealth case that function turns out to be a straight line, which is what we would get in the limit of large population if we had used a step function. Lewis Goudy ( talk) 16:14, 25 March 2017 (UTC)
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I agree, I had trouble learning about the Lorenz curve from this page because the cdf is different. The cdf plots the cumulative % of the variable against the category. The Lorenz plots the cumulative % of the variable against the cumulative % of population (calculated from the categories). The first sentence and the graph labeling should be revised. —Preceding unsigned comment added by Intlthahc ( talk • contribs) 20:37, 12 January 2008 (UTC)
Is it really a "cumulative" dist. fn. ?? The the y-axis gives the sum as a PERCENTAGE of the total, whereas in the cdf, the y-axis will give the un-normalized sum. This will produce a logrithmic-shaped graph rather than an exponential one... Nigel, May 7, 2006
Nigel, after sorting individuals from poorest to richest, the point (x,y), tells us the cumulative number of individuals (on the x-axis) and the cumulative wealth of those individuals (y-axis). A cumulative distribution function would put wealth (not cumulative) on the x-axis and number of people (cumulative) on the y-axis.
Polymer scientists approach the distribution of polymer molecular weights in a polymer samples (same concept as distribution of wealth among individuals) in yet another way. We talk about number distributions and weight distributions (neither one cumulative), often use logarithmic scales for the molecular weight, and use the ratio of the weight average molecular weight to the number average as a measure of dispersity. I would not be surprised to hear of other fields that treat mathematically equivalent problems in still other ways. I suspect that "least confusing" depends on precisely what one's question is and/or what one is already familiar with -- Emil M Friedman — Preceding unsigned comment added by Emilfriedman ( talk • contribs) 18:11, 23 September 2014 (UTC)
The curve is apparently always convex. Is there any corner case that it's not convex? — Preceding unsigned comment added by 74.117.104.162 ( talk) 12:30, 23 October 2019 (UTC)
If the variable being measured can take negative values but has a positive mean, then the Lorenz curve will sink below the line of perfect inequality and is a convex function.
If the variable being measured can take negative values and has a negative mean, then the Lorenz curve will be above the line of perfect equality, except at the end points, and is a concave function.
^ I've edited this out. This convex statement is BS. It can easily be non convex and still be monotonic increasing. The graph pictured is misleading. Jasmine85 ( talk) 10:07, 3 September 2009 (UTC)
The Lorenz curve is convexe and not concave as is said in the text, see the graph below.
Can we get a real life example for the illustration from some place? Paranoid 20:10, 6 Jan 2005 (UTC)
The Lorenz Curve is used in geography as well to represent unequal distribution of the world's population over area...please add that in
'... we call this line the line of perfect equality or the 45° line.' It's only 45° when both axes have equal scales.
Holy Cow 20:55, 18 March 2006 (UTC)
What does a Lorenz curve look like for a discrete probability function? What are the formulas for calculating the curve in such a case? DCary 04:19, 26 May 2006 (UTC)
Is x(F), the inverse of F(x), equal F-1(f(x))? -- Kwj2772 ( talk) 13:21, 17 July 2009 (UTC)
The article waffles back and forth on whether this curve typically represents income or wealth, which are completely distinct measures. Which one is kind of important. -- 75.94.164.123 ( talk) 14:11, 28 June 2011 (UTC)
would like an explanation (it may have been buried in the math, didn't look) as to why the curve cannot hump above the perfect equality line when non-negative variables are used. It would seem that a decreasing increase is possible. — Preceding unsigned comment added by Barnsward ( talk • contribs) 19:42, 15 August 2011 (UTC) never mind, i see that if all are lined up in ascending order on the x axis there has to be an increasing increase. — Preceding unsigned comment added by 69.123.186.12 ( talk) 23:17, 15 August 2011 (UTC)
Is there a proof of the below, can some one add citation, or simply prove it.
In "Definition and calculation" section: Please define Fi, Si, and Li; or at least F, S, and L. I couldn't find any "...where S equals..." Thank you 71.139.166.86 ( talk) 23:12, 22 February 2014 (UTC)
I think the image found here is very helpful. It shouldn't be difficult for someone with basic skills in graph making (which I lack) to recreate it in a free version. -- Piotr Konieczny aka Prokonsul Piotrus| reply here 09:08, 29 April 2014 (UTC)
The real world sample graphic isn't showing Denmark at all, contrary to its caption. Lewis Goudy ( talk) 16:00, 25 March 2017 (UTC)
In the case of perfectly equal wealth distribution, why is the lorenz curve considered to be a straight line? For example, in that case, how would you decided which 10% of the population is the "bottom" 10% ? As a mathematical technicality, don't we have to assume that individuals with equal wealth will be ranked in some arbitrary order?
Tashiro~enwiki ( talk) 15:34, 9 October 2016 (UTC)
The independent variable is not the set of individuals but rather the size of that set as a fraction of the size of the total population. We are modeling a discrete situation using continuous mathematics, so we represent the cumulative presentation as a piecewise linear function rather than a step function. In the equal wealth case that function turns out to be a straight line, which is what we would get in the limit of large population if we had used a step function. Lewis Goudy ( talk) 16:14, 25 March 2017 (UTC)