R package extWeibQuant: Estimate Lower Extreme Quantile with the Censored Weibull MLE and Censored Weibull Mixture. It implements the subjectively censored Weibull MLE and censored Weibull mixture methods for the lower quantile estimation. Quantile estimates from these two methods are robust to model misspecification in the lower tail. It also includes functions to evaluation the standard error of the resulting quantile estimates. Also, the methods here can be used to fit the Weibull or Weibull mixture for the Type-I or Type-II right censored data.