stors (version 1.0.1)

srbeta_custom: Sampling from Beta Distribution

Description

The srbeta_custom() function generates random samples from a Beta distribution using the STORS algorithm. It employs an optimized proposal distribution around the mode and Adaptive Rejection Sampling (ARS) for the tails.

Usage

srbeta_custom(n = 1, x = NULL)

Value

A numeric vector of length n containing random samples from the Beta distribution. The shape1 and shape2 parameters are specified during the optimization process using srbeta_optimize().

NOTE: When the x parameter is specified, it is updated in-place with the simulation for performance reasons.

Arguments

n

Integer, length 1. Number of samples to draw.

x

(optional) Numeric vector of length \(n\). If provided, this vector is overwritten in place to avoid any memory allocation.

TODO : This density instead of this function.

This function samples from a proposal constructed using srbeta_optimize, employing the STORS algorithm.

By default, srbeta_custom() samples from the standard Beta distribution with shape1 = 1 and shape2 = 1. The proposal distribution is pre-optimized at package load time using srbeta_optimize() with steps = 4091, creating a scalable proposal centred around the mode.

Details

The Beta Distribution

The Beta distribution has the probability density function (PDF): $$f(x | \alpha, \beta) = \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha)\Gamma(\beta)} x^{\alpha - 1} (1 - x)^{\beta - 1}, \quad 0 \leq x \leq 1,$$ where:

\(\alpha\)

is the first shape parameter (\(\alpha > 0\)).

\(\beta\)

is the second shape parameter (\(\beta > 0\)).

The Beta distribution is widely used in Bayesian statistics and in modelling probabilities and proportions.

See Also

srbeta_optimize to optimize the custom proposal.

Examples

# Generate 10 samples from Beta Distribution
samples <- srbeta_custom(10)
print(samples)

# Generate 10 samples using a pre-allocated vector
x <- numeric(10)
srbeta_custom(10, x = x)
print(x)