Linganisha mbinu

	Uchanganuzi wa Poisson na Negative Binomial	Makadirio ya Eneo dogo (Mfumo wa Fay-Herriot)
Nyanja	Ekonometriki	Metodolojia ya Dodoso
Familia	Regression model	Regression model
Mwaka wa asili	1998	1979
Mwanzilishi	Cameron & Trivedi (textbook treatment); Hilbe (negative binomial)	Robert Fay & Roger Herriot
Aina	Generalized linear model for count data	Model-based survey estimator
Chanzo asilia	Cameron, A. C. & Trivedi, P. K. (1998). Regression Analysis of Count Data. Cambridge University Press.	Fay, R. E., & Herriot, R. A. (1979). Estimates of income for small places: An application of James-Stein procedures to census data. Journal of the American Statistical Association, 74(366), 269–277.
Majina mbadala	count regression, log-linear count model, negative binomial regression, Poisson / Negatif Binom Regresyon	SAE, Model-Based Small Area Estimation, Area-Level Model, Küçük Alan Tahmini
Zinazohusiana	4	2
Muhtasari	Poisson regression is a generalized linear model for count outcomes — events tallied as non-negative integers such as hospital admissions, accidents, or article counts. It models the log of the expected count as a linear function of the predictors, and is developed in the standard count-data treatment of Cameron and Trivedi (1998); when the counts are over-dispersed, the closely related negative binomial model (Hilbe, 2011) is preferred.	Small Area Estimation (SAE) refers to statistical techniques that produce reliable estimates for subpopulations — geographical regions, demographic groups, or administrative units — where direct survey samples are too sparse to yield acceptable precision. The Fay-Herriot model, introduced by Robert Fay and Roger Herriot in 1979, is the canonical area-level SAE model. It supplements weak direct survey estimates with auxiliary covariate information through an empirical Bayes or BLUP framework, substantially reducing mean squared error for small domains.