---
title: "copulaSQM"
output: github_document
---

# copulaSQM

Copula-Based Stochastic Frontier Quantile Model

---

## Description

`copulaSQM` implements a copula-based stochastic frontier quantile model
using the asymmetric Laplace distribution (ALD) and simulated likelihood
estimation.

The model extends classical stochastic frontier analysis (SFA) by:

- Estimating conditional quantile frontiers  
- Allowing asymmetric error distributions  
- Modeling dependence between noise and inefficiency via copulas  

This framework is suitable for applied production analysis,
efficiency measurement, and heterogeneous performance evaluation.

---

## Model

The production model is:

\[
Y_i = X_i \beta + V_i - U_i
\]

where:

- \( V_i \) follows an asymmetric Laplace distribution  
- \( U_i \ge 0 \) is a one-sided inefficiency term  
- Dependence between \( V_i \) and \( U_i \) is modeled using
  copulas available in `VineCopula`  

---

## Installation

```r
# install.packages("devtools")
devtools::install_github("woraphonyamaka/copulaSQM")

library(copulaSQM)
