M_OEM function

The M-OEM algorithm replaces M-step with stochastic step, which is used to solve the parameter estimation of Poisson mixture model.

M_OEM(y, K, alpha0, lambda0, a, b)

Arguments

• y: is a data vector
• K: is the number of Poisson distribution
• alpha0: is the initial value of the mixing weight
• lambda0: is the initial value of the mean
• a: represents the power of the reciprocal of the step size
• b: indicates that the M-step is not implemented for the first b data points

Returns

M_OEMtime,M_OEMalpha,M_OEMlambda

Examples

library(stats)
set.seed(637351)
K=5 
alpha1=c(rep(1/K,K)) 
lambda1=c(1,2,3,4,5) 
n=300 
U=sample(c(1:n),n,replace=FALSE)
y= c(rep(0,n)) 
for(i in 1:n){
if(U[i]<=0.2*n){
y[i] = rpois(1,lambda1[1])} 
else if(U[i]>0.2*n & U[i]<=0.4*n){
y[i] = rpois(1,lambda1[2])} 
else if(U[i]>0.4*n & U[i]<=0.6*n){
y[i] = rpois(1,lambda1[3])} 
else if(U[i]>0.6*n & U[i]<=0.8*n){
y[i] = rpois(1,lambda1[4])}
else if(U[i]>0.8*n ){
y[i] = rpois(1,lambda1[5])} 
}
M=5
seed=637351
set.seed(123) 
e=sample(c(1:n),K)
alpha0=e/sum(e)
lambda0=c(1.5,2.5,3.5,4.5,5.5)
a=0.75
b=5
M_OEM(y,K,alpha0,lambda0,a,b)