Area under a PDF curve

Hi all!

I have a brief question. I am trying to obtain the area under a PDF curve. Concretely, the PDF follows a Lognormal distribution with paremeter mu=0 and sigma=0.9.

zmax=10;
gridz=600;
m=0;
sig=0.9;

z=logspace(0,log(zmax)/log(10),gridz);
g=lognpdf(z,m,sig);

trapz(z,g)

However, the value I obtain is equal to 0.49, far from 1. Any advise please?

Thanks in advanced,

Ibai

[Torsten]

z consists of 600 times the same value, namely 1...

[Ibai Ostolozaga Falcon]

Sorry!

There was a typo in the code that I posted. I have just edited. Once I have changed it, any advise please?

[Torsten]

The first element in the z-vector is z(1)=1.

To get trapz(z,g)=1, you will have to start with z(1) = small value > 0.

So

z = linspace(1e-8,10,gridz)

instead of

z=logspace(0,log(zmax)/log(10),gridz)

should work.

[Ibai Ostolozaga Falcon]

Hi Torsten,

Thank you for your answer! Using linspace and starting at 0, gives me back a value very close to one.

However, I would like to ask why when z(1)=0 gives back a value close to one and when I use z(1)=1 not. That is, when I am building the pdf I am giving to Matlab a grid with 600 points that goes from 1 to 10.

Thank you in advanced.

[Torsten]

However, I would like to ask why when z(1)=0 gives back a value close to one and when I use z(1)=1 not.

The area under the PDF curve between 0 and 1 is 0.5.

Answer 1

[Chunru]

For pdf that matlab supports, you can use cdf function to find the area under pdf. For your case

zmax=10;
m=0;
sig=0.9;

logncdf(zmax, m, sig)

ans = 0.9947