Dhruba, my points are: 1) There are distributions of positive univariates in which part of receptors receive nothing. It means that the total distributed mass finished without reaching all population. 2) If you graph the CDF this appears as a section with variable zero at the left of the CDF graph if ordered in ascense, or at the right extreme if ordered in descense. 3) In the descending model I use, it is determined first a SEM called W=ln(L i)/ln(p i) that may be represented as a continuous soft proxy function. So Lorenz curve is L= p^W(p); for 1>= W(p) >= 0, so when W(p)=0, L becomes 1, and there is no more to distribute, so I decided to declare that L value becomes 1 for any W

Dear Dhruba, take a look here:

http://en.wikipedia.org/wiki/Finite_difference

and here:

http://en.wikipedia.org/wiki/Divided_differences

You can define what each time is more suitable for computations.

Actually sir, if i have to find dy/dx and d^2/dx^2 at x=1, then how can I proceed from the following table by constructing a central difference table

x: 1 2 4 8 10

y: 0 1 5 21 27

Dhubra. If we assume that x and y values you give are mean values of 1/5 population intervals, then this may mean that for x mean =1, variable y does not exist, but for the rest it does fine. I will work models for descending ordering of x and y, and try to find the slopes you mention. I will show it here later to discuss the point. Your question is necessary and perhaps it is a frequent situation for researchers. Thanks, emilio

Thanks sir.

Respected Emilio Chaves, please if it is possible explain me your standpoint a little bit.

Dhruba, my points are: 1) There are distributions of positive univariates in which part of receptors receive nothing. It means that the total distributed mass finished without reaching all population. 2) If you graph the CDF this appears as a section with variable zero at the left of the CDF graph if ordered in ascense, or at the right extreme if ordered in descense. 3) In the descending model I use, it is determined first a SEM called W=ln(L i)/ln(p i) that may be represented as a continuous soft proxy function. So Lorenz curve is L= p^W(p); for 1>= W(p) >= 0, so when W(p)=0, L becomes 1, and there is no more to distribute, so I decided to declare that L value becomes 1 for any W

Thank you sir for your kind response.

Nice question!