apop_normal.c File Reference

Variables

Detailed Description

The Normal and Lognormal distributions.

Variable Documentation

The lognormal distribution.

You know it, it's your attractor in the limit, it's the Gaussian distribution.

As is custom, the first parameter is the mean, the second is the standard deviation (i.e., the square root of the variance).

The log likelihood function and dlog likelihood don't care about your rows of data; if you have an 8 x 7 data set, it will give you the log likelihood of those 56 observations given the mean and variance you provide.

$N(\mu,\sigma^2) = {1 \over \sqrt{2 \pi \sigma^2}} \exp (-x^2 / 2\sigma^2)$

$\ln N(\mu,\sigma^2) = (-(x-\mu)^2 / 2\sigma^2) - \ln (2 \pi \sigma^2)/2$

$d\ln N(\mu,\sigma^2)/d\mu = (x-\mu) / \sigma^2$

$d\ln N(\mu,\sigma^2)/d\sigma^2 = ((x-\mu)^2 / 2(\sigma^2)^2) - 1/2\sigma^2$

The apop_ls settings group includes a want_cov element, which refers to the covariance matrix for the mean and variance. You can set that to 'n' if you are estimating millions of these and need to save time (i.e. Apop_model_add_group(your_model, apop_ls, .want_cov = 'n');).

Apophenia

apop_normal.c File Reference

Variables

Detailed Description

Variable Documentation