Is alexa rank increase it's good thing or bad

There is no valid motivations that even make sense for me to make it up? I'll have a look at references but you would probably disregard them as not "credible" anyways. You need to understand, that if you gave your input properly in the first place, it would have been more heavily respected and would have made a bigger statement to people who will search up this question in the future. It just feels you're bitter over something you could have corrected rather than just attacked.

Anyways back on topic, OP it doesn't have as much influence as it use to. That's the straight forward answer.

 

In general terms, the lower the number the better. However, how Alexa actually calculates your 'rank' is a grey area and has nothing to do with Google. I really wouldn't worry about it at all

 

Don't take Alexa ranking seriously. It doesn't directly reflect to your overall SEO efforts.
If you want to improve your rankings then focus on your target audience, marketing strategies and the onpage optimization of your site.