approx_mvn_at_time: Approximate Multivariate Normal Distribution as Beta at a...

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Approximate Multivariate Normal Distribution as Beta at a Specific Time

Description

Converts a multivariate normal distribution for Weibull parameters (or a mixture of these distributions) into an approximate beta distribution for the survival probability at a specific time point. This is particularly useful for visualizing survival probabilities in sweet spot plots

Usage

approx_mvn_at_time(x, time)

Arguments

x	A vector of distributional objects that must be either multivariate normal distributions or mixtures of multivariate normal distributions. For Weibull models, these represent distributions of the log(shape) and log(scale) parameters.
time	A numeric value specifying survival time at which to calculate the survival probability.

Details

The function performs the following steps:

• For each multivariate normal distribution, it generates 10,000 samples of the Weibull parameters

• Calculates the corresponding survival probabilities at the specified time using the Weibull survival function

• Fits a beta distribution to match the mean and variance of these survival probabilities

• For mixture distributions, it performs this approximation for each component and creates a new mixture with the same weights

The conversion uses the relationship between Weibull parameters and survival probability: S(t) = exp(-(t*exp(log_scale))^exp(log_shape)).

Value

A vector of beta distributional (or mixture of beta distributional) objects approximating the survival probabilities at the specified time point. If the input is a mixture distribution, the output will be a mixture of beta distributions with the same weights.

See Also

sweet_spot_plot()

Examples

library(distributional)

# Create a multivariate normal distribution for Weibull parameters
# (log(shape), log(scale))
mvn_dist <- dist_multivariate_normal(
  mu = list(c(0, -1)),  # log(shape) = 0, log(scale) = -1
  sigma = list(matrix(c(0.1, 0, 0, 0.1), nrow = 2))
)

# Approximate as beta distribution for survival at time t=12
beta_approx <- approx_mvn_at_time(mvn_dist, time = 12)

beastt documentation built on June 8, 2025, 11:42 a.m.