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This vignette demonstrates the application of
UniLindleyApprox to 14 benchmark probability distributions
across survival analysis, reliability theory, and computational
statistics literature:
library(UniLindleyApprox)
# Weibull PDF, CDF, Survival (theta = c(shape, scale))
dweibull_custom <- function(x, theta) dweibull(x, shape = theta[1], scale = theta[2])
pweibull_custom <- function(x, theta) pweibull(x, shape = theta[1], scale = theta[2])
sweibull_custom <- function(x, theta) 1 - pweibull(x, shape = theta[1], scale = theta[2])
# Independent Gamma log-prior for shape and scale
logprior_weibull <- function(theta) {
if (theta[1] <= 0 || theta[2] <= 0) return(-Inf)
dgamma(theta[1], shape = 2, rate = 1, log = TRUE) +
dgamma(theta[2], shape = 2, rate = 1, log = TRUE)
}
# Simulated progressive Type-II data
obs <- c(0.5, 1.2, 1.8, 2.5, 3.1)
R <- c(2, 0, 1, 0, 2)
data_prog <- list(observed = obs, removal_scheme = R, n_total = 10)
fit_weibull <- lindley_fit(
data = data_prog,
pdf = dweibull_custom,
cdf = pweibull_custom,
survival = sweibull_custom,
log_prior = logprior_weibull,
theta0 = c(1.5, 2.0),
scheme = "progressive_type2",
loss = "SELF",
control = lindley.control(verbose = FALSE)
)
summary(fit_weibull)
#> Summary of Bayesian Estimation Using Lindley's Approximation
#> ============================================================
#>
#> Model Information:
#> Censoring Scheme: progressive_type2
#> Loss Function: SELF
#> Number of Parameters: 2
#>
#> Parameter Estimates:
#> Parameter MAP Bayes_Estimate Posterior_Mean
#> theta1 1.745905 1.789724 1.789724
#> theta2 2.723526 3.014287 3.014287
#>
#> Model Fit:
#> Log-Likelihood: -10.3624
#> Log-Posterior: -13.2726
#> AIC: 24.7248
#> BIC: 22.922
#>
#> Optimization:
#> Convergence: Successful
#> Iterations: 15
#> Elapsed Time: 0.02 seconds
#>
#> Information Matrix:
#> [,1] [,2]
#> [1,] 2.811730 -0.075062
#> [2,] -0.075062 2.827562The 1-parameter Lindley distribution has PDF \(f(x) = \frac{\theta^2}{1 + \theta} (1 + x) e^{-\theta x}\) for \(x > 0, \theta > 0\).
dlindley_custom <- function(x, theta) {
th <- theta[1]
if (th <= 0 || any(x <= 0)) return(rep(0, length(x)))
(th^2 / (1 + th)) * (1 + x) * exp(-th * x)
}
plindley_custom <- function(x, theta) {
th <- theta[1]
1 - (1 + (th * x) / (1 + th)) * exp(-th * x)
}
slindley_custom <- function(x, theta) 1 - plindley_custom(x, theta)
set.seed(123)
x_lindley <- rexp(40, rate = 1.5)
fit_lindley <- lindley_fit(
data = x_lindley,
pdf = dlindley_custom,
cdf = plindley_custom,
survival = slindley_custom,
log_prior = function(th) dgamma(th[1], 2, 1, log = TRUE),
theta0 = c(1.0),
scheme = "complete",
loss = "LINEX",
control = lindley.control(verbose = FALSE)
)
print(fit_lindley)
#> Bayesian Estimation Using Lindley's Approximation
#> ================================================
#>
#> Censoring Scheme: complete
#> Loss Function: LINEX
#>
#> Posterior Mode (MAP):
#> [1] 2.032641
#>
#> Bayes Estimate (LINEX):
#> [1] 2.03515
#>
#> Posterior Mean:
#> [1] 2.067922
#>
#> Log-Likelihood: -21.8484
#> Log-Posterior: -23.1717
#> Convergence: Successful
#> Iterations: 14
#> Elapsed Time: 0.02 secondsThese binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.