Analysis and remediation of the confusing specification of the lognormal distribution

Purpose
The lognormal distribution is by far the most frequent distribution type to model uncertainty in LCA data. Its parameterization is non-trivial, and there are various options for this, some of which employ confusing names and symbols. The result is that by now many different systems have emerged, including ambiguous and incorrect forms.

Methods
Here, we clarify the situation by studying the approaches in textbooks on probability and statistics, LCA documents on uncertainty, LCA databases, LCA software, and often-used programming and simulation tools.

Results and discussion
One of our conclusions is that the representation of the lognormal distribution in LCA is done in a very heterogeneous, confusing, and sometimes contradicting or inconsistent way. Even high-profile organizations (such as ISO) and widely used databases (such as ecoinvent) which aim to harmonize practice are unclear or ambiguous about the way they represent the parameters of the lognormal distribution. A final issue of concern is the use of units in relation to those parameters. If one source specifies a lognormally distributed variable in kilogram, how should a system working with gram process those parameters? Also here, the answer is surprisingly hard and we expect that mistakes with this may have been made in case studies and databases.

Conclusions
We end by proposing a consistent and unambiguous system of parameters to communicate a lognormally distributed variable.