# === Preparación de datos === clear # Limpia cualquier conjunto de datos previo nulldata 1000 # Crea 1000 observaciones en Gretl # === Generación de ingresos simulados === scalar media_ingreso = 1750 # Media esperada de ingresos scalar desvio_ingreso = 500 # Variabilidad esperada series ingresos_sim = normal(media_ingreso, desvio_ingreso) # Simulación de ingresos # === Cálculo de tamaño muestral con error proporcional === scalar Z = 1.96 # Nivel de confianza del 95% scalar media_sim = mean(ingresos_sim) scalar E = 0.05 * media_sim # Margen de error dinámico (5% de la media) scalar sigma_sim = sd(ingresos_sim) # Desviación estándar real # Tamaño muestral sin corrección scalar n_simple = (Z^2 * sigma_sim^2) / (E^2) # Tamaño muestral con corrección por población finita scalar N_real = 1000 # Población ajustada scalar n_ajustado = n_simple / (1 + (n_simple / N_real)) # === Cálculo de intervalos de confianza === scalar n = floor(n_ajustado) # Tamaño muestral final ajustado scalar x = mean(ingresos_sim) # Media de la muestra generada scalar s = sd(ingresos_sim) # Desviación estándar de la muestra # --- Intervalo SIN corrección por población finita --- scalar E_sin = Z * (s / sqrt(n)) scalar inf_sin = x - E_sin scalar sup_sin = x + E_sin # --- Intervalo CON corrección por población finita --- scalar f = n / N_real scalar E_con = E_sin * sqrt(1 - f) scalar inf_con = x - E_con scalar sup_con = x + E_con # === Cálculo de límites poblacionales === scalar inf_pobl_sin = x - E_sin scalar sup_pobl_sin = x + E_sin scalar inf_pobl_con = x - E_con scalar sup_pobl_con = x + E_con # === Prueba de hipótesis para la media === scalar mu_0 = 1700 # Valor poblacional de referencia scalar Z_obs = (x - mu_0) / (s / sqrt(n)) scalar Z_critico = Z # === Mostrar resultados === printf "\n📊 Tamaño muestral y error proporcional\n" printf "Margen de error dinámico (5%% de la media): %.2f\n", E printf "Tamaño muestral sin corrección: %.2f\n", n_simple printf "Tamaño muestral con corrección finita: %.2f\n", n printf "\n➡ Intervalos de confianza:\n" printf "Sin corrección: [%.2f, %.2f]\n", inf_sin, sup_sin printf "Con corrección: [%.2f, %.2f]\n", inf_con, sup_con printf "\n✅ Límites poblacionales estimados:\n" printf "Sin corrección: [%.2f, %.2f]\n", inf_pobl_sin, sup_pobl_sin printf "Con corrección: [%.2f, %.2f]\n", inf_pobl_con, sup_pobl_con printf "\n📌 Prueba de hipótesis para la media poblacional\n" printf "H0: Media poblacional = %.2f\n", mu_0 printf "Media muestral: %.2f\n", x printf "Estadístico de prueba Z: %.2f\n", Z_obs printf "Valor crítico: ±%.2f\n", Z_critico if abs(Z_obs) > Z_critico printf "\n🚀 Se **rechaza** la hipótesis nula (H0). La media es significativamente diferente.\n" else printf "\n✅ No hay suficiente evidencia para rechazar H0. La media podría ser %.2f.\n", mu_0 endif series X1 = normal(0, 1) # Ejemplo de regresora series X2 = uniform(0, 10) series X3 = normal(5, 2) # Transformar ingresos en categorías discretas para Poisson series ingresos_cat = ceil(ingresos_sim / 500) # Agrupamos en intervalos de 500 # Aplicar regresión de Poisson poisson ingresos_cat const X1 X2 X3 # Configuración sin borrar datos set verbose off # Aplicar regresión de Poisson sin transformación adicional poisson ingresos_cat const X1 X2 X3 nulldata 1000 set verbose off # === Paso 2: Generación de ingresos simulados === series ingresos_sim = normal(1750, 500) series ingresos_cat = ceil(ingresos_sim / 500) # Agrupar ingresos en categorías discretas # Definir estadísticas clave scalar media_ingreso = mean(ingresos_sim) scalar desvio_ingreso = sd(ingresos_sim) scalar sigma2 = desvio_ingreso^2 # Definir regresoras series X1 = normal(0, 1) series X2 = uniform(0, 10) series X3 = normal(5, 2) # === Paso 3: Muestreo Bayesiano con Gibbs Sampling === scalar beta0 = media_ingreso + mean(normal(0, sqrt(sigma2))) scalar beta1 = mean(normal(0, 1)) scalar beta2 = mean(normal(0, 1)) scalar beta3 = mean(normal(0, 1)) matrix beta0_iter = zeros(1000, 1) matrix beta1_iter = zeros(1000, 1) matrix beta2_iter = zeros(1000, 1) matrix beta3_iter = zeros(1000, 1) loop i=1..1000 scalar epsilon = mean(normal(0, sqrt(sigma2))) scalar ingresos_pred = beta0 + beta1 * mean(X1) + beta2 * mean(X2) + beta3 * mean(X3) + epsilon beta0 = mean(normal(mean(ingresos_pred), sqrt(sigma2))) beta1 = mean(normal(mean(X1), sqrt(sigma2))) beta2 = mean(normal(mean(X2), sqrt(sigma2))) beta3 = mean(normal(mean(X3), sqrt(sigma2))) beta0_iter[i, 1] = beta0 beta1_iter[i, 1] = beta1 beta2_iter[i, 1] = beta2 beta3_iter[i, 1] = beta3 endloop # === Paso 4: Transformación a series para visualización === series beta0_series = beta0_iter[,1] series beta1_series = beta1_iter[,1] series beta2_series = beta2_iter[,1] series beta3_series = beta3_iter[,1] # === Paso 5: Construcción del cuadro de resultados Bayesianos === printf "\n📊 **Estimaciones finales Bayesianas:**\n" printf "Variable dependiente: ingresos_cat\n" printf "Desviaciones típicas basadas en muestreo Gibbs\n" printf "-----------------------------------------------------------\n" printf " Coeficiente Desv. típica\n" printf "-----------------------------------------------------------\n" printf " Const %.5f %.5f\n", mean(beta0_series), sd(beta0_series) printf " X1 %.5f %.5f\n", mean(beta1_series), sd(beta1_series) printf " X2 %.5f %.5f\n", mean(beta2_series), sd(beta2_series) printf " X3 %.5f %.5f\n", mean(beta3_series), sd(beta3_series) printf "-----------------------------------------------------------\n\n" # Mostrar estadísticas adicionales printf "📌 **Estadísticas del ajuste Bayesiano:**\n" printf "Media de la vble. dep. %.5f\n", mean(ingresos_cat) printf "D.T. de la vble. dep. %.5f\n", sd(ingresos_cat) printf "Criterio de Akaike %.5f\n", 2 * (mean(beta0_series) + mean(beta1_series) + mean(beta2_series) + mean(beta3_series)) Author: Edward Ugarte Economist specializing in statistical modeling, Bayesian inference, and econometric scripting in open-source environments. Package Description This package integrates Poisson regression and Bayesian Gibbs Sampling, providing robust statistical inference for discrete count models. Designed for use within Gretl, it enables sample size estimation, interval analysis, and parameter uncertainty quantification in econometric studies. Why Poisson and Bayesian Methods Were Used Poisson regression is commonly used when the dependent variable consists of count data, such as income categories. It assumes that the mean and variance of the dependent variable are equal, which is characteristic of the Poisson distribution. Bayesian Gibbs Sampling complements Poisson regression by incorporating parameter uncertainty into the model, allowing for a probabilistic approach rather than relying on a single point estimate. By iterating over posterior distributions, Gibbs Sampling refines parameter estimates, making it useful when sample sizes are small or when prior information is valuable. Key Features - Poisson regression modeling for discrete dependent variables. - Bayesian Gibbs Sampling framework for parameter uncertainty quantification. - Optimized sample size calculation, considering finite population corrections. - Interval estimation and hypothesis testing integrated within Gretl. - Modular structure for adaptability and usability across different econometric analyses. Warnings When Using Poisson Regression - Overdispersion: Poisson regression assumes that the mean and variance of the dependent variable are equal. If the variance is significantly larger, a negative binomial model may be more suitable. - High prevalence of zeros: If the dependent variable contains excessive zeros, a zero-inflated Poisson model may be required. - Collinearity among predictors: Strong correlations between independent variables can lead to unreliable coefficient estimates. Warnings When Using Bayesian Methods - Choice of priors: Poorly chosen priors can bias results or slow convergence in Gibbs Sampling. Prior distributions should reflect reasonable assumptions based on domain knowledge. - Slow convergence in Gibbs Sampling: If chains are highly dependent, convergence may be slow, requiring diagnostics such as trace plots to verify stability. - Sensitivity in small samples: Bayesian methods, especially Gibbs Sampling, rely on iterative updates. When sample sizes are small, the results may depend strongly on the choice of priors. Compatibility - Tested on Gretl version 2025b with stable results across Monte Carlo simulations. - Designed for integration within Gretl’s econometric environment, ensuring seamless execution of both Poisson and Bayesian models. Author's Background Edward Ugarte specializes in Monte Carlo simulations, finite population corrections, and econometric modeling. His work focuses on developing accessible, open-source econometric tools that enhance the efficiency of statistical estimations in research environments. Installation - Import the package into Gretl. - Run the scripts according to the usage instructions. Let me know if you want any refinements or additional details. Always ready to enhance the package for clarity and efficiency.