fit_dist function

Fit a general distribution to observations

The default implementation performs maximum likelihood estimation on all placeholder parameters.

fit_dist(dist, obs, start, ...)

fit_dist_direct(dist, obs, start, ..., .start_with_default = FALSE)

## S3 method for class 'Distribution'
fit(object, obs, start, ...)

Arguments

• dist: A Distribution object.
• obs: Set of observations as produced by trunc_obs() or convertible via as_trunc_obs().
• start: Initial values of all placeholder parameters. If missing, starting values are obtained from fit_dist_start().
• ...: Distribution-specific arguments for the fitting procedure
• .start_with_default: Before directly optimising the likelihood, use an optimised algorithm for finding better starting values?
• object: same as parameter dist

Returns

A list with at least the elements

• params the fitted parameters in the same structure as init.
• logLik the final log-likelihood

Additional information may be provided depending on dist.

Details

For Erlang mixture distributions and for Mixture distributions, an EM-Algorithm is instead used to improve stability.

fit() and fit_dist() will chose an optimisation method optimized for the specific distribution given. fit_dist_direct() can be used to force direct maximisation of the likelihood.

Examples

x <- rexp(100)
lambda_hat <- 1 / mean(x)
lambda_hat2 <- fit_dist(dist_exponential(), x)$params$rate
identical(lambda_hat, lambda_hat2)
dist <- dist_mixture(list(dist_normal(), dist_translate(dist_exponential(), offset = 6)))
params <- list(
  dists = list(list(mean = 5, sd = 1), list(dist = list(rate = 1))), probs = list(0.95, 0.05)
)
set.seed(2000)
u <- runif(100, 10, 20)
x <- dist$sample(100, with_params = params)
obs <- trunc_obs(x = x[x <= u], tmin = -Inf, tmax = u[x <= u])

default_fit <- fit_dist(dist, obs)
direct_fit <- fit_dist_direct(dist, obs)
# NB: direct optimisation steps with pre-run take a few seconds

direct_fit_init <- fit_dist_direct(dist, obs, start = default_fit$params)
direct_fit_auto_init <- fit_dist_direct(dist, obs, .start_with_default = TRUE)

stopifnot(direct_fit_init$logLik == direct_fit_auto_init$logLik)

c(default_fit$logLik, direct_fit$logLik, direct_fit_init$logLik)

See Also

Other distribution fitting functions: fit_blended(), fit_erlang_mixture(), fit_mixture()

Other distribution fitting functions: fit_blended(), fit_erlang_mixture(), fit_mixture()