Continuous laplacian random variable

I want to plot the outcomes of a Laplacian random Variable when i have the type : A>=sqrt(sigma^2/2)*ln(1/0.01) with sigma=1.I understand what i need to plot but i can not understand that how can I present discrete values for 50 trials ..?Could anyone suggest me how can I do it ?

Thanks!

Answer 1

[Tom Lane]

Take a look at this:

sigma = 1;
p = rand(10000,1);
A=sqrt(sigma^2/2)*log(1./p);
hist(A,100)

I'm not sure if it's what you want. It uses random P in place of the 0.1 value from your expression. Otherwise it uses that expression to generate random numbers, and makes a histogram of them. Notice that I use "./" to perform division on every element of P.

Perhaps you can figure out how to present the result of 50 trials by looking at this.

[John Agkali]

Thanks for your time !!But this is what i would like to represent with matlab <img153.imageshack.us/img153/1733/exampledi.jpg>...if you know how,that will be great !(If you can't see the photo, just copy-paste the link in the Address bar)

[Tom Lane]

sigma = 1;
p = rand(50,1);
A=sign(rand(50,1)-.5).*sqrt(sigma^2/2).*log(1./p);
stem(A)

Here I'm conjecturing that the distribution you want is described by the formula for A, but with a random sign and with 0.1 replaced by a uniform random number. The formula you give for A is just a single numeric value. It is described as the clipping level in the image you provided.

I encourage you to think about this code fragment, understand it, and make sure it's what you want. You should be able to superimpose +/- the clipping level if you need to do that.

[John Agkali]

First of all, thank you once again ! In order to understand it better, every time i run this code i got different outcomes based on rand()..But what does sign function do ? Is this last photo going to help http://img196.imageshack.us/img196/918/laplacianrandomvariable.png ?

It says under the diagramm about a inverse probability integral transformation.Is this the way I am going to represent the outcomes of a Laplacian Variable? I would be grateful if you could help me, this time too..

[Tom Lane]

As I understand it, the Laplace distribution is the so-called double exponential distribution. If X has a Laplace distribution then, with probability 1/2 of each, either X or -X has an exponential distribution.

So, sign(rand(...)-.5) is either +1 or -1, each with probability 1/2.

[John Agkali]

Could you explain to me how *sign *function works? Why do i need it ?

[Tom Lane]

You need to find some way to get either a positive or a negative sign. This is one way. It produces the result +1 when its input is positive, and -1 when its input is negative.

[John Agkali]

The first code segment that you gave me, the one with function hist in it, could you briefly tell me what a histogramm represents ? How can i "decode" its meaning ? And for what purposes is used ?

For example,if I hist the function in the second code segment that you sent me, hist(A), what can I describe about that ? Is there something very important about histogramm I should know ?

Thank you!!

[Tom Lane]

The image you posted showed each trial as a dot, plotted with a line connecting it to zero. That works fine with the 50 or so trials you have.

I had lots of trials so I made a histogram. It counts the number of trials in each of several bins, and draws a bar of that height. So the heights of the bars give a picture of the distribution of points across bins. It may be this is not important for what you are trying to do.