fit_dist {reservr}

Fit a general distribution to observations

Description

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

Usage

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

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.

Value

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.

See Also

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

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

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)