I'm a newcomer to Maxima. I'm really delighted to find this, and I intend
to learn to use it well because, since it's GPL'd, no one will ever be able
to take it away from me! Thanks to everyone who's contributed to it.
I'm a statistician, so run into summations (over observed data points)
often. I seem to be running into some walls regarding manipulating
summations.
I've been practicing with a well-known, simple example: demonstrating that
the average is the maximum likelihood estimator for the mean of a Gaussian
series of observations (independent and having common parameters mu and
sigma). I'll use Latex notation. Here are a few questions:
(If you wish to send me information off-list, please send it to this
address and to my home address, jim_garrett@comcast.net.)
1. Suppose I define the log-likelihood function for a single data point
$x_i$ (the log-likelihood is the log of the probability density function
for the observations, regarding the observed data as fixed and the
parameters--mu and sigma here--as varying):
loglik_1 : log(1/sqrt(2 * %pi) * exp(-1/2 * (x[i] - mu)^2));
Now if I see $x_1, x_2, \ldots, x_n$ data observations, the log-likelihood
for the sequence is obtained by adding loglik_1, with a difference $i$ each
time. I tried
loglik : sum(loglik_1, i, 1, 10);
but that gave me 10 * loglik_1 for a single arbitrary $i$. How can I
communicate that each term in the summation is different?
2. Moving on, I meet something of this form:
\[ \sum_{i = 1}^n (x_i - \mu) = 0. \]
In order to solve for mu, I want to make this into two summations:
\[ \sum_{i = 1}^n (x_i - \mu) = \sum_{i = 1}^n x_i - \sum_{i = 1}^n \mu.
\]
How can I do that?
3. Can Maxima realize that for one summation it's summing a constant,
i.e., $\sum_{i = 1}^n \mu = n \mu$?
I'm sure I'll have more questions later on. These are standard things that
arise in statistics, so once I figure this out I'll be able to advise other
statisticians with a "design pattern", if you will.
Thanks for any advice.
Jim Garrett
Becton Dickinson Diagnostic Systems
Baltimore, Maryland, USA
**********************************************************************
This message is intended only for the designated recipient(s). It may
contain confidential or proprietary information and may be subject to
the attorney-client privilege or other confidentiality protections.
If you are not a designated recipient, you may not review, use, copy
or distribute this message. If you receive this in error, please
notify the sender by reply e-mail and delete this message. Thank you.
***********************************************************************