Probability density and RNG function for the mixture of shifted lognormal and uniform distributions.

Usage

rshifted_lognormal_uniform(
  n,
  meanlog = 0,
  sdlog = 1,
  mix = 0.1,
  shift = 0,
  max_uniform = 100
)

dshifted_lognormal_uniform(
  y,
  meanlog = 0,
  sdlog = 1,
  mix = 0.1,
  shift = 0,
  max_uniform = 100
)

Source

Some background, discussion and examples at http://www.martinmodrak.cz/2021/04/01/using-brms-to-model-reaction-times-contaminated-with-errors/

Arguments

n: the number of values to draw from the RNG
meanlog: the mean of the lognormal component
sdlog: the sd of the lognormal component
mix: the probability of the value comming from the uniform component
shift: the shift the lognormal distribution
max_uniform: the maximum value of the uniform component
y: the observed value

Details

The mixture of shifted lognormal and uniform can be described as $$y_i = \begin{cases} u_i & \mathrm{if} \quad z_i = 0 \\ s_i + r_i & \mathrm{if} \quad z_i = 1 \end{cases} \\ u_i \sim Uniform(0, \alpha) \\ \log(r_i) \sim Normal(\mu_i, \sigma) \\ P(z_i = 0) = \theta$$

Where θ corresponds to mix, α to max_uniform and $s_i$ to shift.