# Probability density and distribution function

I am new to probability course and find concepts very confusing. I am learning maximum likelihood estimation and as a starting point for that do we find the density or the distribution?

In general, do we find the distribution from density or is it vice versa and how does one find it? For example, for Gaussian distribution do we find the density of a variable or the distribution so as to estimate unknown parameter A in the case x[n] = A + w[n] where w[n] are uncorrelated gaussian noise. This may sound too trivial but I am really confused. In many contexts I have come across where pdf = prob. density function and in some areas I find pdf = prob distribution function !!

• You're asking several different questions here. Commented Jun 13, 2014 at 4:28

I am learning maximum likelihood estimation and as a starting point for that do we find the density or the distribution?

The likelihood is written as a product of pdfs or pfs (aside from when dealing with things like censoring).

In general, do we find the distribution from density or is it vice versa

It depends on what you have and what you need.

and how does one find it? For example, for Gaussian distribution do we find the density of a variable or the distribution so as to estimate unknown parameter A in the case x[n] = A + w[n] where w[n] are uncorrelated gaussian noise.

You'd neither find the density or the distribution. Typically you'd assume normality and estimate the parameters. You might use a diagnostic to help assess the suitability of that assumption, and you might look at the comparison between a sample cdf and a theoretical one, or at some representation of a density (histogram or kde), but often people tend to look at a Q-Q plot to assess normality.

This may sound too trivial but I am really confused. In many contexts I have come across where pdf = prob. density function and in some areas I find pdf = prob distribution function !!

That can happen, and it's confusing, but the second form is fortunately very rare. Typically, pdf means density and cdf generally means distribution.

• Yes, I saw the question when you posted it. The reason I didn't give a response is it's not a question I've ever considered in enough depth to attempt an answer. It's a fascinating question, and if I had a good answer to it I would have posted one. Commented Jun 13, 2014 at 22:13
• I'm not watching a video for you, sorry. If you can transcribe the critical information into your question, perhaps I'll have a close look. But Gaussian distributions don't all have 0 mean. It's actually a family, with two parameters - the mean $\mu$ and variance $\sigma^2$. Commented Jun 14, 2014 at 5:25