6.7.10. statsmodels.sandbox.regression.tools¶
gradient/Jacobian of normal and t loglikelihood
use chain rule
normal derivative wrt mu, sigma and beta
new version: loc-scale distributions, derivative wrt loc, scale
also includes “standardized” t distribution (for use in GARCH)
TODO: * use sympy for derivative of loglike wrt shape parameters
it works for df of t distribution dlog(gamma(a))da = polygamma(0,a) check polygamma is available in scipy.special
- get loc-scale example to work with mean = X*b
- write some full unit test examples
A: josef-pktd
6.7.10.1. Functions¶
locscale_grad(y, loc, scale, dlldy, *args) |
derivative of log-likelihood with respect to location and scale |
mean_grad(x, beta) |
gradient/Jacobian for d (x*beta)/ d beta |
norm_dlldy(y) |
derivative of log pdf of standard normal with respect to y |
norm_lls(y, params) |
normal loglikelihood given observations and mean mu and variance sigma2 |
norm_lls_grad(y, params) |
Jacobian of normal loglikelihood wrt mean mu and variance sigma2 |
normgrad(y, x, params) |
Jacobian of normal loglikelihood wrt mean mu and variance sigma2 |
ts_dlldy(y, df) |
derivative of log pdf of standard t with respect to y |
ts_lls(y, params, df) |
t loglikelihood given observations and mean mu and variance sigma2 = 1 |
tstd_dlldy(y, df) |
derivative of log pdf of standardized t with respect to y |
tstd_lls(y, params, df) |
t loglikelihood given observations and mean mu and variance sigma2 = 1 |
tstd_pdf(x, df) |
pdf for standardized (not standard) t distribution, variance is one |