% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/estimation_bayes.R
\name{bayes_mtl}
\alias{bayes_mtl}
\title{Bayesian Estimation for the Modified Topp-Leone Distribution}
\usage{
bayes_mtl(
  x,
  prior = c("informative", "noninformative"),
  a = 1,
  b = 1,
  loss = c("self", "elf", "plf", "gelf", "all"),
  delta = 1,
  n.draws = 10000,
  burn.in = 1000,
  thin = 1,
  conf.level = 0.95
)
}
\arguments{
\item{x}{Vector of sample observations (\code{x > 0}).}

\item{prior}{Type of prior distribution: \code{"informative"} (Gamma(a, b)) or \code{"noninformative"} (\code{a = 0, b = 0}).}

\item{a}{Shape parameter for Gamma prior (hyperparameter \code{a > 0}).}

\item{b}{Rate parameter for Gamma prior (hyperparameter \code{b > 0}).}

\item{loss}{Loss function: \code{"self"} (Squared Error Loss), \code{"elf"} (Entropy Loss),
\code{"plf"} (Precautionary Loss), \code{"gelf"} (Generalized Entropy Loss), or \code{"all"}.}

\item{delta}{Constant for Generalized Entropy Loss Function (\code{delta != 0}). Default is 1.}

\item{n.draws}{Number of MCMC iterations (default: 10000).}

\item{burn.in}{Number of initial draws to discard as burn-in (default: 1000).}

\item{thin}{Thinning interval for MCMC chain (default: 1).}

\item{conf.level}{Credible level for HPD interval estimation (default: 0.95).}
}
\value{
A list containing point estimates under specified loss functions, posterior standard error (PSE),
posterior summary statistics, MCMC sample draws, and the 100*(1 - alpha)\% HPD interval.
}
\description{
Estimates the shape parameter \code{alpha} of the Modified Topp-Leone (MTL) distribution
under informative (Gamma) and non-informative priors using symmetric (SELF) and asymmetric
(ELF, PLF, GELF) loss functions, along with Chen-Shao Highest Posterior Density (HPD) intervals.
}
\examples{
set.seed(123)
sample_data <- rmtl(n = 30, alpha = 2.5)

# Bayesian Estimation under Non-informative Prior
bayes_mtl(x = sample_data, prior = "noninformative", loss = "all")

# Bayesian Estimation under Informative Prior (a = 2, b = 1)
bayes_mtl(x = sample_data, prior = "informative", a = 2, b = 1, loss = "self")

}
\references{
Singh, B., Tyagi, S., Singh, R. P., and Tyagi, A. (2025). Modified Topp-Leone
Distribution: Properties, Classical and Bayesian Estimation with Application to COVID-19
and Reliability Data. \emph{Thailand Statistician}, 23(1), 72-96.

Chen, M. H., and Shao, Q. M. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals.
\emph{Journal of Computational and Graphical Statistics}, 8(1), 69-92.

Calabria, R., and Pulcini, G. (1996). Point estimation under asymmetric loss functions for left-truncated
exponential samples. \emph{Communications in Statistics - Theory and Methods}, 25(3), 585-600.
}
\author{
Shikhar Tyagi, Abhishek Tyagi, Arvind Pandey, Bhupendra Singh, Vrijesh Tripathi
}
