Davidian curves in R

A Davidian curve defines a seminonparametric density, whose shape and flexibility can be tuned by easy to estimate parameters. Since a special case of a Davidian curve is the standard normal density, Davidian curves can be used for relaxing normality assumption in statistical applications [1].

This package provides the density function, the gradient of the loglikelihood and a random generator for Davidian curves:

  1. ddc(x, phi), Davidian curve density function
  2. rdc(n, phi), a random sampler for Davidian curves
  3. dc_grad(x, phi), the gradient function of Davidian curves

The second argument phi of these functions is a vector, which contains the parameter(s) of a Davidian curve. The higher the number of parameters, the more flexible the density. The values of the parameres define the shape of the curve. Following [1, 2], this package provides support for Davidian curves up to 10 parameters.


  1. Zhang, D., & Davidian, M. (2001). Linear mixed models with flexible distributions of random effects for longitudinal data. Biometrics, 57(3), 795-802.
  2. Woods, C. M., & Lin, N. (2009). Item response theory with estimation of the latent density using Davidian curves. Applied Psychological Measurement, 33(2), 102-117.