Can anyone tell me why the Page Rank and Alexa Rank of my website has dropped down?

[Claudia J]

And to get it back what all effort I have to implement?

[Joseph]

Not without seeing the site...

[Jake]

Google page rank is mainly based on backlinks from other sites, if you have lost links from sites that have vanishing, have been lowered in rank themselves, it's possible that a review of your sit has caused more backlinks to be discredited and labeled unnatural, adding more outgoing links tend to leak link juice, though links to authority sites add to your credibility, it's hard to guess from your 2 sentences.

Alexa rank is based on measured traffic, using data collected from a small sampling of users.

Only if you are selling a site are those rankings really all that important, search ranking for desirable keywords tends to more directly correlate to site success.

[Isabella]

Google has done an update(Google Algorithm Update) on Jan 17th 2013, and there has been a major drop in rankings as well as traffic.

All latest Google SEO updates of 2013:
Update 1 on 17 January 2013 – Google Algorithm Update
Update 2 on 22 January 2013 – Google Panda Algorithm Update #24
Update 3 on 25 January 2013 – Google Page Rank Update
Update 4 on 27 January 2013 - Google Rolled Back Its Recent Google Algorithm Updates
Update 6 on 4 February 2013 – Google Page Rank Update

Any one of these updates may have affected your ranking.

[Reet]

Its hard to explain without looking at website. Must be because of penguin or panda update...

[Tim Nash]

Multiple factors are responsible in dropping down the Page ranking and alexa ranking. First check the quality of back links, whether they are of good quality. There many online tools are present through which you can you can figure out what exactly is wrong with your website. One more this thing you can do, by taking the help of an expert SEO company, as they are use to of getting ranking back to websites. One of my friends hired the services of SEO Leaders Ltd. and he told me they are the best in the SEO industry. So you better contact them once as well.

Regards
Tim