This repository contains a Stan model for analyzing report delay data using a mixture of distributions: Weibull, Gamma, and Lognormal. The model aims to estimate the parameters of these distributions and their weights in the mixture.

The model requires the following data:

N: Integer, the number of observations.

report_delay[N]: Real array, the observed report delays.

The model estimates the following parameters:

sd_delay: Standard deviation of the delay (positive real).

param1_weibull: Shape parameter for the Weibull distribution (positive real).

weight: Simplex of length 3, representing the weights of the three distributions in the mixture.

The model computes several transformed parameters:

param1_delay[3]: Shape parameters for the Gamma, Weibull, and Lognormal distributions.

param2_delay[3]: Scale parameters for the Gamma, Weibull, and Lognormal distributions.

mean_delay: Mean of the delay, computed from sd_delay and param1_weibull.

lps[3]: Log probabilities for each distribution in the mixture.