Mathematical Statistics

Appendix A:Symbolism

Partially we distinguish in notation from other mathematical disciplines. We do not use capital letters as in probability theory to denote random variables but denote them by bold printing. We do this not only to distinguish between a random variable F with F‐distribution and its realisation F but mainly because linear models are important in this book. In a mixed model in the two‐way cross‐classification of the analysis of variance with a fixed factor A and a random factor B, the model equation with capital letters is written as

This looks strange and is unusual. We use instead

Functions are never written without an argument to avoid confusion. So is p(y) often a probability function but p a probability. Further is f(y) a density function but f the symbol for degrees of freedom.

Sense	Symbol
Rounding‐up function	⌈x⌉ = smallest integer
Binomial distribution with parameters n, p	B(n,p)
Chi‐squared (χ2) distribution with f degrees of freedom	CS (f)
Determinant of the matrix A	|A|, det(A)
Diagonal matrix of order n	diag(a1, …, an)
Direct product of the sets A and B
Direct sum of the sets A and B
Identity matrix of order n	In
(