I would suggest you take a look at this page on MozTrust. As the name indicates, MozTrust is an tool which measures trust factors for a website.
MozTrust and PR are similar metrics. They are both attempts to determine a site's importance and credibility. The largest factor is your site's ability to earn credible external links from other credible sites.
Example 1- you create a natural viagra-like sex supplement using common ingredients from other similar pills. You set up an e-commerce site and sell your product. It will likely take you a long time (i.e. years) to build up trust unless you pour an enormous amount of resources (i.e. money) into the site.
Example 2 - you create a natural viagra-like sex supplement based on credible research from UC Berkeley or another credible institution. You perform authentic studies by doctors and the results are published in the New England Journal of Medicine and other credible medical journals. The doctors and researchers involved in the study all post numerous articles on your site, and respond to questions.
As a result of the above activities, the New York Times, CNN and other credible news sources cover the story and link to your site. Additionally the doctors involved with the study are asked to be interviewed on Oprah and other television shows. All the media hype turns into hundreds of links from highly credibly sites and a lot of social media buzz.
The second example can help a brand new site very quickly earn a lot of trust. Then the product begins selling, authentic testimonials are received, further research is performed, more doctors and patients begin working with the product, leading to even more credibility and trust.