srgamma_custom | R Documentation |
The srgamma_custom()
function generates random samples from a Gamma distribution using the STORS algorithm.
It employs an optimized proposal distribution around the mode and Adaptive Rejection Sampling (ARS) for the tails.
srgamma_custom(n = 1, x = NULL)
n |
Integer, length 1. Number of samples to draw. |
x |
(optional) Numeric vector of length |
The Gamma Distribution
The Gamma distribution has the probability density function (PDF):
f(x | \alpha, \beta) = \frac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha - 1} \exp(-\beta x), \quad x \geq 0,
where:
\alpha
is the shape parameter (\alpha > 0
), which determines the shape of the distribution.
\beta
is the rate parameter (\beta > 0
), which determines the rate of decay.
The Gamma distribution is widely used in statistics, particularly in Bayesian inference and modelling waiting times.
This function samples from a proposal constructed using srgamma_optimize
, employing the STORS algorithm.
By default, srgamma_custom()
samples from the standard Gamma distribution with shape = 1
and rate = 1
.
The proposal distribution is pre-optimized at package load time using srgamma_optimize()
with
steps = 4091
, creating a scalable proposal centred around the mode.
A numeric vector of length n
containing random samples from the Gamma distribution.
The shape
and rate
parameters are specified during the optimization process using srgamma_optimize()
.
NOTE: When the x
parameter is specified, it is updated in-place with the simulation for performance reasons.
This function is not scalable. Therefore, only the srgamma_custom()
version is available, which requires the proposal to be pre-optimized using srgamma_optimize()
before calling this function.
srgamma_optimize
to optimize the custom proposal.
# Generate 10 samples from Gamma Distribution
samples <- srgamma_custom(10)
print(samples)
# Generate 10 samples using a pre-allocated vector
x <- numeric(10)
srgamma_custom(10, x = x)
print(x)
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