Misprints plague us all. To remove misprints we read and reread, and we try to coerce others into reading. The issue is, when can we declare victory?
In this article we do two things: first, we summarize the background for determining the probability distribution of misprints in a manuscript, then we provide a table of the distribution function from which you may determine the probabilities for misprints in your manuscript.
Let n represent a number of misprints per page and let Pn be the probability of finding n misprints on any page. We assume the following:
There are a couple of other more technical assumptions, but they rarely apply for our problem, so I will not bother you with them. In our situation, the original question (When victory?), therefore, really has to do with the probability of rare events; events that are expected to occur infrequently, but which have an impact when they do occur.
Under these assumptions, the probability Pn for n misprints per page is given by the Poisson distribution,
Pn = kn exp[– k]/n!
where k = average number of misprints per page. When the average k gets large, then the Poisson distribution collapses to a Gaussian. To compute a probability from the Poisson distribution, you must collect some data from your ms; in particular, you need an estimate for k.
R. W. Hamming, The Art of Probability for Scientists and Engineers, Addison-Wesley, Redwood, CA, 1991.
W. E. Deming, Some Theory of Sampling, Dover, New York, 1966; reprint of 1950 edition published by Wiley.