pseudo_values {MixedPoisson}

Pseudo values – Expectation-Maximization (EM) algorithm

Description

The function returns the pseudo values t_i defined as the conditional expectation E[\theta_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

\lambda parameter in mixed Poisson model

gamma.par

\gamma parameter in Gamma mixing distribution

nu

\nu parameter in log-normal mixing distribution

delta

\delta 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[\theta_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 \gamma, \nu, \delta 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)