Owing to the rich shapes of Generalised Lambda Distributions (GLDs), GLD standard/quantile/Accelerated Failure Time (AFT) regression is a competitive flexible model compared to standard/quantile/AFT regression. The proposed method has some major advantages: 1) it provides a reference line which is very robust to outliers with the attractive property of zero mean residuals and 2) it gives a unified, elegant quantile regression model from the reference line with smooth regression coefficients across different quantiles. For AFT model, it also eliminates the needs to try several different AFT models, owing to the flexible shapes of GLD. The goodness of fit of  the proposed model can be assessed via QQ plots and Kolmogorov-Smirnov tests and data driven smooth test, to ensure the appropriateness of the statistical inference under consideration. Statistical distributions of coefficients of the GLD regression line are obtained using simulation, and interval estimates are obtained directly from simulated data.  References include the following: Su (2015) "Flexible Parametric Quantile Regression Model" <doi:10.1007/s11222-014-9457-1>, Su (2021) "Flexible parametric accelerated failure time model"<doi:10.1080/10543406.2021.1934854>.

Fits a generalized linear density ratio model (GLDRM).
    A GLDRM is a semiparametric generalized linear model.
    In contrast to a GLM, which assumes a particular exponential family distribution, 
    the GLDRM uses a semiparametric likelihood to estimate the reference distribution. 
    The reference distribution may be any discrete, continuous, or mixed exponential 
    family distribution. The model parameters, which include both the regression 
    coefficients and the cdf of the unspecified reference distribution, are estimated 
    by maximizing a semiparametric likelihood. Regression coefficients are estimated 
    with no loss of efficiency, i.e. the asymptotic variance is the same as if the 
    true exponential family distribution were known.
    Huang (2014) <doi:10.1080/01621459.2013.824892>.
    Huang and Rathouz (2012) <doi:10.1093/biomet/asr075>.
    Rathouz and Gao (2008) <doi:10.1093/biostatistics/kxn030>.