Here are 6 best ways to improve PR and Alexa ranking,

1. Right keyword selection
2. Forum Posting
3. Blog commenting
4. Article Submission
5. Social Bookmarking
6. Directory Submission
What you think?

I am totally agree with you..In off site factors we have to do atleast all these steps if we want to improve our site ranking quickly. As well as right keyword is also very important. Keep it up.

It is very much possible to increase the PR using the mentioned techniques, however, it doesn't have any connection with Alexa. Alexa ranking is defined through the Alexa toolbar installed on each of the browser through which a particular website is visited.

Factors you have stated are link building tips and PR can be increased "only" by "quality backlinks". As far as Alexa is concerned, Alexa ranking is assigned to only those who have "alexa toolbar" installed on their machines.
Had I been you, I wouldn't have bothered about PR or Alexa since they are mere popularity metrics. Google has over 200+ factors which are considered while ranking.
I prefer the bigger picture that is ranking in SERPs.

yes i think these tips are best for any website success but i think you didn't mentioned that link should be from related niche ,dofollow and high pr pages..........

These are good tips to get good pagerank for your website.

All ways are really cool and awesome for PR.

Well,thanks for providing useful information...I really like this kind of informative posts...Please keep sharing like these useful information with us...Keep it up..