From Algorithms to Z-Scores - matloff - University of California, Davis

144 CHAPTER 7. COVARIANCE AND RANDOM VECTORS
• mean: the mean vector
• sigma: the covariance matrix
• lower, upper: bounds for a multidimensional “rectangular” region of interest
Since a multivariate normal distribution is characterized by its mean vector and covariance matrix,
the first two arguments above shouldn’t suprise you. But what about the other two?
The function finds the probability of our random vector falling into a multidimensional rectangular
region that we specify, through the arguments are lower and upper. Note that these will typically
be specified via R’s c() function, but default values are recycled versions of -Inf and Inf, built-in
R constants for −∞ and ∞.
An important special case is that in which we specify upper but allow lower to be the default
values, yielding:
just what we need to find P (X ≤ 12 and Y ≤ 16).
P (W1 ≤ c1, ..., Wr ≤ cr) (7.61)
To account for the integer nature of X and Y, we call the function with upper limits of 12.5 and 16.5,
rather than 12 and 16, which is often used to get a better approximation. (Recall the “correction
for continuity,” Section 5.5.2.9.) Our code is
1 p1