Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications

A.2 FURTHER READING

There does not appear to be a single reference containing all of the information in this appendix. The reader can find many of these results in the probability books listed in the bibliography at the end of this book. Perhaps the following books are most useful, especially for moments and other properties of the univariate distributions: Johnson, Kemp, and Kotz (2005), Johnson, Kotz, and Balakrishnan (1994), and Johnson, Kotz, and Balakrishnan (1995). Some additional references with summaries include: Krishnamoorthy (2006), Mood, Graybill, and Boes (1974), Pal, Jin, and Lim (2006), Peebles (1993), Weisstein (2003), Yates and Goodman (2005), and Zwillinger and Kokoska (2000).

Although we do not summarize results here for the multivariate distributions covered in Chapter 4, the reader might find the following references useful: Gumbel (1960), Johnson, Kotz, and Balakrishnan (1997), Kotz, Balakrishnan, and Johnson (2000), and Mardia (1970).

Most of the expressions for differential entropy can be found in Verdugo Lazo and Rathie (1978).

Finally, we provide a few references for specific distributions that are not widely discussed in many textbooks on probability. Half-normal: Leone, Nelson, and Nottingham (1961). Inverse Gaussian: Chhikara and Folks (1989) and Seshadri (1999). Laplace: Kotz, Kozubowski, and Podgórski (2001). Logistic: Balakrishnan, Ed. (1992). Lognormal: Limpert, Stahel, and Abbt (2001). Weibull: Rousu (1973).