I like to think that I have good statistical horse sense, but that’s no substitute for knowing the subject properly. I’m seeking suggestions on good statistics texts. Longtime readers know that I’m not afraid of math, but in this case, I’m not especially interested in reading proofs of the most general case or derivations of the closest bounds possible. Instead, I’d like to learn:

- Essential theory and notation of random variables and distributions with a reasonable degree of rigor.
- The most significant distributions in a statistician’s toolkit, with good coverage of their distinguishing properties.
- A well-explained treatment of statistical inference that discusses choice among tests of significant and necessary assumptions.
- Some queueing theory, with an emphasis on the decisions that inform one’s choice of model.
- Across all of the above, a satisfyingly elegant treatment of the common mathematical techniques that statisticians use when trying to understand the world, predict outcomes, simplify messy calculations, and minimize error terms.

I could go to the library and start pulling, or go online and read lots of reviews, but I figure that the readership here may have some better suggestions of particularly nice books on these topics.