Feller, William. An Introduction to Probability Theory and Its Applications, Vol. 1 (discrete distributions), 3rd ed. 1968. Vol. 2 (continuous distributions), 2nd ed. 1971. Wiley. The standard reference of probabilists. It is a serious mathematical treatment of the subject, but includes numerous examples and exercises designed to develop the reader's intuition in the art of probabilistic formulation.
Kendall, Sir Maurice; Stuart, Alan; and Ord, J. Keith. The Advanced Theory of Statistics,
Volume 1, Distribution Theory, 5th ed., 1987.
Volume 2, Inference and Relationship, 5th ed., 1991
Volume 3, Design and Analysis and Time Series, 4th ed., 1983.
Oxford University Press and Charles Griffin & Co. Ltd.
Excellent reference books. They are useful to the person who wants only an overview as well as the one who wants to explore the deeper concepts involved.
Statistics Journals with mostly survey or expository articles:
For statistics journals with mostly technical articles, review the "publications" lists of the ASA and the IMS from their websites given above.
Useful books at a lower level:
The authors listed below are those used by UT Austin's mathematics, business, and statistics departments in undergraduate courses over the last decade or so. Earlier editions of these are easily available to borrow from libraries or to purchase fairly inexpensively.
Undergraduate Mathematical Statistics
Wackerly, Mendenhall, and Scheaffer. Mathematical Statistics with Applications
Elementary Statistics for an "upper division" audience
Moore, David and McCabe, George. Introduction to the Practice of Statistics
Deveaux, Velleman, and Bock: Statistics: Data and Models
Elementary Statistics for a "lower division" audience
Deveaux, Velleman, and Bock Intro Stats
Moore, David Basic Practice of Statistics
Last updated August 23, 2014 . Mary Parker