From the Social Science Statistics Blog, a post asking How to Take the Log of Zero Income:

I am encountering a question when using a Log normal distribution to model income distribution. Namely, there are a bunch of people in my dataset who report zero income, maybe due to unemployment, and I am wondering how to logarize the zero incomes.

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Vineet, on March 10, 2009 at 11:50 am said:Depends on the scale he’s using for income mapping. E.g: Rs. 143, 678 is A’s income.

1. Let’s suppose he’s using the income as it is. So, log(143, 678) will be computed. This ways an income between 0 and 1 doesn’t look to be practical. So, he shud approximate Zero income as zero as well.

2. In case it’s being scaled. e.g: our example becomes 0.143678 millons, then he’s have to use -ve infty. for lof of zero income, as there’d be negative values anyways.

Basically try and keep the log of Zero income the best left most possible value on the x-axis.

Improvements/ suggestions would be welcome