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