As you are doing Analysis yes PAST is good but I personally recommend you to use IBM SPSS for measuring  diversities index and other ecological index because these are quantitative analysis and SPSS is a good tool for statistical analysis.You can use PAST but SPSS can make you analysis better and broader.Although SPSS is a proprietary software but I recommend it for better and easy understanding analysis through it's broad community .You can ask for analysis help to any SPSS related discussion websites and groups also you can find the SPPS software (19) latest version in any sharing websites or torrent sites.Thanks.Can check for also Matlab(matrix laboratory) analysis,communities for these type indexing.

R would be great for this as well. I personally use the Vegan package (https://cran.r-project.org/web/packages/vegan/index.html) in R for diversity calculations. And just as the person stated for SPSS, R is a software that would allow you to explore different aspects and do other things beyond vegetation analyses. R like SPSS also has lots of online forums, support, and tutorials. 

It depends what analyses you want to perform. Past is helpful in many ways, especially for calculations of diversity indices and species accumulation curves. You may also want to know about EstimateS, another free software available online at viceroy.eeb.uconn.edu/estimates/

If you know how to program in R, you may like this even better, because you can not only use code written by others but also add your own code for specific analyses.

Other commercial programs (you have to purchase) for multivariate analyses and ordinations are PRIMER at http://www.primer-e.com/ and PC-ORD at https://www.pcord.com/

thank you for your help!

As Klaus said, PAST is useful to analyze vegetation data, it is free and very easy to use. EstimateS also helps you to estimate some parameters that you mentioned (but with the correction proposed by Chao et al. 2005 especially for similarity indices). With those two programs you does not need anything else to perform these analysis (I use these two programs to analyze data for one published paper). But if you have notion of writing programming code R is the better option (with fossil package). SPSS like PRIMER and PC-ORD are a commercial programs, so you need purchase the licenses to use legally.

I place two links. I hope this information will be useful for you.

I put two links then you could be useful

Best regards

Cristian

http://viceroy.eeb.uconn.edu/estimates/EstimateSPages/EstSUsersGuide/References/ChaoEtAl2005.pdf

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