saddlepoint

saddlepoint provides a general framework for saddlepoint approximation (SPA) where distributions and model components are represented by cumulant generating functions (CGFs) and their derivatives. It supports saddlepoint likelihood evaluation and parameter estimation for composite and high-dimensional constructions.

Saddlepoint methods use the CGF $K(t) = \log \mathbb{E}\left[\exp(t X)\right]$ to build accurate approximations to likelihoods, densities, and tail probabilities.

Key functionalities we provide

• CGF objects for common families (e.g., Poisson, Gamma, Gaussian, Binomial, Negative Binomial, Multinomial).
• Operators to build new CGFs by composition (e.g., i.i.d. replication, linear maps, sums, random sums, tilting operations, etc).
• Likelihood tools for saddlepoint-based inference, including workflows for maximum likelihood estimation.
• Error/discrepancy computations

Quick start: saddlepoint MLE for a simple model

library(saddlepoint)
set.seed(1)

y <- rnorm(60, mean = 2, sd = 1.5)

fit <- find.saddlepoint.MLE(
  observed.data  = y,
  cgf            = NormalCGF,
  starting.theta = c(mu = 0, sigma = 1),
  lb.theta       = c(-Inf, 1e-8),
  ub.theta       = c( Inf, Inf),
  method         = "two_step",   
  std.error      = TRUE
)

fit$MLEs.theta
fit$std.error