No predefined R function exists for $S(t)$, but we can take advantage of the fact that $$S(t)=1-F(t)$$
For $\;T \sim Weibull(\beta,\theta)$
$S(t)=$ 1 - pweibull(q = quantile, shape = shape param, scale = scale param)
For $\;T \sim Exponential(\lambda)$
$S(t)=$ 1 - pexp(q = quantile, rate = rate parameter)
For $\;T \sim Normal(\mu,\sigma)$
$S(t)=$ 1 - pnorm(q = quantile, mean = mean, sd = standard deviation)
For $\;T \sim Lognormal(\mu,\sigma)$
$S(t)=$ 1 - plnorm(q = quantile, meanlog = log(mean), sdlog = log(stdev))
For $T \sim Gamma(\kappa,\beta)$
$S(t)=$ 1-pgamma(q = quantile, shape = shape param, scale = scale param)
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