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#' @title Expected Value for Positive Poisson Distribution
#'
#' @description
#' Computes the expected value from a Poisson (PP) distribution based on the model parameters and covariates.
#'
#' @param b Numeric vector of coefficients for the Poisson model.
#' @param X Matrix of predictors for the Poisson model, where rows correspond
#' to observations and columns to covariates.
#'
#' @return
#' A numeric vector of expected values for each observation in the dataset.
#'
#' @seealso
#' \code{\link{dEdq_pois_noinfl}} for computing partial derivatives of expected values in the Poisson model.
#'
#' @keywords internal
E_pois_noinfl <- function(b, X) {
l <- exp(X %*% b)
w <- 0
w + (1 - w) * l * exp(l) / (exp(l) - 1)
}
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