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I am trying to compute the value of $\bar F(x)=1-F(x)$ where F(X) is the generalized Gamma distribution. I found that this distribution is also called the equilibrium distribution of Weibull. Someone knows a package in R to compute this cumulative probability? or how to deal with it?

I found the argument of equilibrium distribution here page 9 https://file.scirp.org/pdf/JMF_2016082314152700.pdf. And actually worked for me I use it to generate random deviates of such density, but now I need to compute the exact value for F(x).

I also was trying to use the method suggested here

How to simulate a random variable with this density?

without success. But I think that is right, now I need to evaluate F(x) for F the equlibrium distribution of Weibull or generalized gamma. that I think that are the same thing.

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This distribution is implemented in the R packages rmutil and flexsurv. Just have a look at them and be careful with the potentially different parametrizations:

http://ugrad.stat.ubc.ca/R/library/rmutil/html/GGamma.html

https://cran.r-project.org/web/packages/flexsurv/flexsurv.pdf

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