For a vector k (p dimensions），Now I want to use a function to evalute the value of \Phi_h (k)-0.5, the h is the bandwith for we use a gaussian kernel density,what I should do for the construct for the function?

Thank you very much .

The CDF of a 1d standard normal distribution is available in Stan as Phi (https://mc-stan.org/docs/2_23/functions-reference/Phi-function.html).

You can do the CDF for a 1d normal with a different mean/standard deviation using the normal cdf (https://mc-stan.org/docs/2_23/functions-reference/normal-distribution.html).

That doesn’t answer your question about the multiple dimensions though. This stuff is only available for the 1d case in Stan.