# Is there a distribution appropriate for a continuous variable skewed toward zero and able to include zero?

I am interested in modelling the impact of some environmental parameters on a concentration of measured phytoplankton pigment. The concentration of pigment is skewed so that low concentrations are more frequent than high ones and there are occasions of 0 (zero) concentration. I was hoping to use a GLM model with a Gamma distribution, but the zero values prevent such a fitting. My question is if there are other options for me.

I thought to simply add a very small number to all concentrations (e.g. 0.00001) and proceed, but perhaps this is ill-advised. Given that the response variable is continuous, I am not sure what my options are - Poisson and Negative Binomial distributions are only for count data?

• Concentrations are almost never exactly zero: if you name almost any molecule, you will likely find it in almost any living thing. Thus, your zeros probably represent positive values that are too small to be detectable. They are therefore left censored. Consider looking for solutions that accommodate censoring. Such solutions typically allow for the variable to be re-expressed: usually, the logarithm is a good choice for environmental concentrations.
– whuber
Oct 26, 2012 at 13:42
• Thank you @whuber - you are right that these zeros are in fact below the detection limit of the instrument. So, when you say that they should be censored, should I leave these out of my analysis (i.e model fitting)? I find this somewhat of a shame given that there is then information lost (albeit I don't know how close to zero these values actually are). Oct 29, 2012 at 13:57
• Marc, "censoring" is the accurate (but perhaps unfortunate) technical term for data that are known only to be less than (or greater) than some threshold. Such data still contain considerable information. It is almost always a mistake to leave them out of an analysis, but it is also almost always a mistake to replace them all by some constant value. "Censored" methods in statistics are those that correctly exploit the information in these kinds of data. Information about some of the approaches is at practicalstats.com/nada.
– whuber
Oct 29, 2012 at 16:59