srpareto_optimize: Optimizing Pareto Distribution proposal

Description

The srpareto_optimize() function generates an optimized proposal for a targeted Pareto Distribution. The proposal can be customized and adjusted based on various options provided by the user.

Usage

srpareto_optimize(
  scale = NULL,
  shape = NULL,
  xl = NULL,
  xr = NULL,
  steps = 4091,
  proposal_range = NULL,
  theta = 0.1,
  target_sample_size = 1000,
  verbose = FALSE
)

Value

The user does not need to store the returned value, because the package internally cashes the proposal. However, we explain here the full returned proposal for advanced users.

A list containing the optimized proposal and related parameters for the specified built-in distribution: #'

data: Detailed information about the proposal steps, including x, s_upper, p_a, and s_upper_lower.
areas: The areas under the left tail, steps, and right tail of the proposal distribution.
steps_number: The number of steps in the proposal.
f_params: The parameters (scale and shape) of the Beta distribution.

Arguments

scale: (optional) Numeric. scale parameter of the Pareto Distribution. Defaults to NULL, which implies a scalable proposal with scale = 1.
shape: (optional) Numeric. shape parameter of the Pareto Distribution. Defaults to NULL, which implies a scalable proposal with shape = 1.
xl: Numeric. Left truncation bound for the target distribution. Defaults to -Inf, representing no left truncation.
xr: Numeric. Right truncation bound for the target distribution. Defaults to Inf, representing no right truncation.
steps: (optional) Integer. Desired number of steps in the proposal. Defaults to NULL, which means the number of steps is determined automatically during optimization.
proposal_range: (optional) Numeric vector. Specifies the range for optimizing the steps part of the proposal. Defaults to NULL, indicating automatic range selection.
theta: Numeric. A parameter for proposal optimization. Defaults to 0.1.
target_sample_size: (optional) Integer. Target sample size for proposal optimization. Defaults to 1000.
verbose: Boolean. If TRUE, detailed optimization information, including areas and steps, will be displayed. Defaults to FALSE.

Details

When srpareto_optimize() is explicitly called:

A proposal is created and cached. If no parameters are provided, a standard proposal is created with rate = 1.
Providing rate creates a custom proposal, which is cached for use with srpareto_custom().
The optimization process can be controlled via parameters such as steps, proposal_range, or theta. If no parameters are provided, the proposal is optimized via brute force based on the. target_sample_size.

Examples

Run this code

# Generate scalable proposal that with rate = 1, that has 4096 steps
scalable_proposal <- srpareto_optimize(steps = 4096)

# Generate custom proposal that with scale = 4
scalable_proposal <- srpareto_optimize(scale = 4)