# Math Help - Looking for a PDF

1. ## Looking for a PDF

Hello,

Does anyone know a probability distribution with the following characteristics:
Univariate
With only one parameter
Supported over the real line (-8,+8)
The expected value can be any real number
...?

For example, the Exponential distribution has all these characteristics but the support over the real line...

Thx a lot

2. Originally Posted by lalohurtado
Hello,

Does anyone know a probability distribution with the following characteristics:
Univariate
With only one parameter
Supported over the real line (-8,+8)
The expected value can be any real number
...?

For example, the Exponential distribution has all these characteristics but the support over the real line...

Thx a lot
I don't see how the expected value can be any real number if the support is a bounded interval .....

3. ## Correction

The support is not bounded... I screwed up by writing "eights" instead of "Infinity" signs...

4. Originally Posted by lalohurtado
The support is not bounded... I screwed up by writing "eights" instead of "Infinity" signs...

No use being impatient when the delay is your own making.

A pdf that satisfies your criteria (the Logistic distribution) can be found here: Logistic distribution - Wikipedia, the free encyclopedia

5. ## Almost, but not quite...

The logistic distribution has two parameters... one for location and another for scale.

Thanks for the reply though...

6. t-distribution.

Or you can construct one. For instance, if X is exponential, then log X is a one-parameter infinite support random variable.

7. ## Txs a lot...

but I'd appreciate some more help...

The t distribution would not work for me because the one-parameter version is centered at 0, and cannot take any real value as Expected value...

I had thought of the log-exponential distribution. But the thing with it is that its expected value is ridiculously difficult to express... and untractable for all practical purposes...

You are right, the log-exponential fits my requirements... but I want to ask for help again to find another distribution that fits my requirements, but with a tractable expression for the expected value.

Sorry for being a pain! but I'll appreciate any help!

8. Take any two-parameter distribution with infinite support, fix one of the parameters to a constant and voila, you have a one-parameter distribution satisfying your requirement.

Seriously though, what's the point of finding such a distribution?