According to one urban legend, statistics depends on the normal distribution and, since most data aren't normally distributed, statistics is invalid.

This myth is easily busted. Many data, including natural phenomena, are in fact normally distributed. Secondly, the normal (Gaussian) distribution is but one of more than three dozen used in statistics. These two books concisely review the ones used most often by statisticians:

- Handbook of Statistical Distributions (Krishnamoorthy)
- Statistical Distributions (Forbes et al.)

As Bayesian statistics becomes mainstream, a good understanding of probability may be more important than ever. I've been cracking the books and have found these three quite helpful:

- Introduction to Probability (Bertsekas and Tsitsiklis)
- Introduction to Probability Models (Ross)
- Essentials of Probability Theory for Statisticians (Proschan and Shaw)

These three provide a somewhat philosophical take on probability:

- Probability, Statistics and Truth (von Mises)
- Probability Theory: The Logic of Science (Jaynes)
- Uncertainty: The Soul of Modeling, Probability & Statistics (Briggs)

Lastly, I'd recommend The Improbability Principle by David Hand to anyone.

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