Archive for the ‘Mathematics’ Category

Using Stata’s random-number generators, part 4, details

For those interested in how pseudo random number generators work, I just wrote something on Statalist which you can see in the Statalist archives by clicking the link even if you do not subscribe:

To remind you, I’ve been writing about how to use random-number generators in parts 1, 2, and 3, and I still have one more posting I want to write on the subject. What I just wrote on Statalist, however, is about how random-number generators work, and I think you will find it interesting.

To find out more about Statalist, see


How to successfully ask a question on Statalist

Using Stata’s random-number generators, part 3, drawing with replacement

The topic for today is drawing random samples with replacement. If you haven’t read part 1 and part 2 of this series on random numbers, do so. In the series we’ve discussed that Read more…

Using Stata’s random-number generators, part 2, drawing without replacement

Last time I told you that Stata’s runiform() function generates rectangularly (uniformly) distributed random numbers over [0, 1), from 0 to nearly 1, and to be precise, over [0, 0.999999999767169356]. And I gave you two formulas,

  1. To generate continuous random numbers between a and b, use

    generate double u = (ba)*runiform() + a

    The random numbers will not actually be between a and b: they will be between a and nearly b, but the top will be so close to b, namely 0.999999999767169356*b, that it will not matter.

  2. To generate integer random numbers between a and b, use Read more…

Using Stata’s random-number generators, part 1

I want to start a series on using Stata’s random-number function. Stata in fact has ten random-number functions: Read more…

The Penultimate Guide to Precision

There have recently been occasional questions on precision and storage types on Statalist despite all that I have written on the subject, much of it posted in this blog. I take that as evidence that I have yet to produce a useful, readable piece that addresses all the questions researchers have.

So I want to try again. This time I’ll try to write the ultimate piece on the subject, making it as short and snappy as possible, and addressing every popular question of which I am aware—including some I haven’t addressed before—and doing all that without making you wade with me into all the messy details, which I know I have a tendency to do. Read more…

Precision (yet again), Part II

In part I, I wrote about precision issues in English. If you enjoyed that, you may want to stop reading now, because I’m about to go into the technical details. Actually, these details are pretty interesting.

For instance, I offered the following formula for calculating error due to float precision: Read more…

Categories: Numerical Analysis Tags: ,

Precision (yet again), Part I

I wrote about precision here and here, but they were pretty technical.

“Great,” coworkers inside StataCorp said to me, “but couldn’t you explain these issues in a way that doesn’t get lost in the details of how computers store binary and maybe, just maybe, write about floats and doubles from a user’s perspective instead of programmer’s perspective?”

“Mmmm,” I said clearly.

Later, when I tried, I liked the result. It contains new material, too. What follows is what I now wish I had written first. I’d would have still written the other two postings, but as technical appendices. Read more…

Categories: Numerical Analysis Tags: ,

Pi is (still) wrong

See this video, by Vi Hart:

This link was passed on to me by my friend Marcello. I’ve been bold enough to make up words such as eigenaxis and eigenpoint, but it takes real courage to suggest redefining π, even when you’re right!

After seeing the video, you can go here and here to learn more about what is being proposed.

Don’t click on comments until you’ve seen the video. Ms. Hart does a better job presenting the proposal than any of us can.

Categories: Mathematics Tags: ,

Understanding matrices intuitively, part 2, eigenvalues and eigenvectors

Last time, I showed you a way to graph and to think about matrices. This time, I want to apply the technique to eigenvalues and eigenvectors. The point is to give you a picture that will guide your intuition, just as it was previously.

Before I go on, several people asked after reading part 1 for the code I used to generate the graphs. Here it is, both for part 1 and part 2: Read more…

Understanding matrices intuitively, part 1

I want to show you a way of picturing and thinking about matrices. The topic for today is the square matrix, which we will call A. I’m going to show you a way of graphing square matrices, although we will have to limit ourselves to the 2 x 2 case. That will be, as they say, without loss of generality. The technique I’m about to show you could be used with 3 x 3 matrices if you had a better 3-dimensional monitor, and as will be revealed, it could be used on 3 x 2 and 2 x 3 matrices, too. If you had more imagination, we could use the technique on 4 x 4, 5 x 5, and even higher-dimensional matrices. Read more…