ald.hpp

// almost word-for-word transcribed from the qrLMM R package

// if you want to operate in unconstrained space,
// mu can be left be
// sigma should be > 0, so log transform
// p should be 0 < p < 1, so logit transform
namespace ald {
    // density function
    template<class Type>
    Type dald(Type y, Type mu, Type sigma, Type p) {
        if (y < mu) {
            return (p * (1 - p)/sigma) * exp((1 - p) * (y - mu)/sigma);
        } else {
            return (p * (1 - p)/sigma) * exp(-p * (y - mu)/sigma);
        }
    }
    
    // quantile function, lower tail only
    template<class Type>
    Type qald(Type prob, Type mu, Type sigma, Type p) {
        if (prob < p) {
            return mu + (sigma * log(prob/p))/(1 - p);
        } else {
            return mu - ((sigma * log((1 - prob)/(1 - p)))/p);
        }
    }
    
    // random number generator
    template<class Type>
    Type rald(Type mu, Type sigma, Type p) {
        Type tmp = runif(0, 1);
        return qald(tmp, mu, sigma, p);
    }
}