Low detection limits are common in measure environmental variables. Building models using data containing low or high detection limits without adjusting for the censoring produces biased models. This paper offers approaches to estimate an inverse Gaussian distribution when some of the data used are censored because of low or high detection limits. Adjustments for the censoring can be made if there is between 2% and 20% censoring using either the EM algorithm or MCMC. This paper compares these approaches.