pseudo_values: Pseudo values - Expectation-Maximization (EM) algorithm

In MixedPoisson: Mixed Poisson Models

Description

The function returns the pseudo values t_i defined as the conditional expectation E[θ_i|k_1,...,k_n], where k_1,...,k_n are realizations of the count variable N.

Usage

pseudo_values(variable, mixing, lambda, gamma.par, nu, delta, n)

Arguments

variable	the vector of numbers
mixing	the name of mixing distribution – "Gamma", "lognorm", "invGauss"
lambda	λ parameter in mixed Poisson model
gamma.par	γ parameter in Gamma mixing distribution
nu	ν parameter in log-normal mixing distribution
delta	δ parameter in inverse-Gaussian mixing distribution
n	The integer value for the Laguerre quadrature. Default to 100

Details

The function calculates the vector of pseudo values t_i=E[θ_i|k_1,...,k_n] in E-step of EM algorithm. It applies the numerical integration using laguerre.quadrature in the nominator and the denominator of the formula

The proper parameter γ, ν, δ should be chosen according to the mixing distribution.

Value

pseudo_values	pseudo values t_1,...,t_n
nominator	nominator in the formula
denominator	denominator in the formula

Author(s)

Alicja Wolny–Dominiak, Michal Trzesiok

Examples

variable=rpois(30,4)
pseudo_values(variable, mixing="Gamma", lambda=4, gamma.par=0.7, n=100)

MixedPoisson documentation built on May 2, 2019, 12:40 p.m.