Three-Parameter Weibull Generator for Replacing Missing Observations

A three-parameter Weibull distribution model was developed and verified to simulate the underlying frequency distributions of observations with missing values through the entire range of observations or near and below detection limit of the monitoring equipment. The corresponding Weibull pseudo-random generator then can be used to estimate and replace the missing observations so that the original distribution of the observations is preserved. This method works very well with any empirical data set with missing observations, distribution of which can be well approximated by a three-parameter Weibull distribution. To demonstrate its applicability, the method was used to estimate and synthetically generate the distribution of hourly ozone (O3) concentrations using the single, weekly mean values obtained from a passive (sodium nitrite absorbent) sampler. The estimation of the Weibull distribution parameters for the synthetic generation of (unavailable) data was based on the data derived from a co-located continuous O3 monitor.