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functions.R
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functions.R
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#CUSUM
cusum = function(x){
res = rep(0, length(x))
meanx = mean(x)
for(i in 2:length(x)){
res[i] = res[i-1] + x[i] - meanx
}
res
}
cusum_plus = function(x){
res = rep(0, length(x))
meanx = mean(x)
for(i in 2:length(x)){
res[i] = max(0, res[i-1] + x[i] - meanx)
}
res
}
cusum_minus = function(x){
res = rep(0, length(x))
meanx = mean(x)
for(i in 2:length(x)){
res[i] = -min(0, -(res[i-1] - x[i] + meanx))
}
res
}
s_i_mean = function(x, theta_0, theta_1){
((x-theta_0)^2)-((x-theta_1)^2)
}
log_like_rat = function(x){
res = rep(0, length(x))
for(i in 1:length(x)){
res[i] = s_i_mean(x[i], mean(x[1:(i-1)]), mean(x[i:length(x)]))
}
res
}
log_like_rat_ln = function(x){
res = rep(0, length(x))
for(i in 1:length(x)){
res[i] = s_i_mean(x[i], lnmean(x[1:(i-1)]), lnmean(x[1:i]))
}
res
}
ratio1 = function(x) {
res = rep(0, length(x))
for(i in 1:length(x)){
res[i] = -(sum((x[1:(i-1)]-mean(x[1:(i-1)]))^2) + sum((x[i:length(x)]-mean(x[i:length(x)]))^2))
}
res
}
ratio2 = function(x) {
res = rep(0, length(x))
for(i in 1:length(x)){
res[i] = (-(sum((x[1:(i-1)]-mean(x[1:(i-1)]))^2) + sum((x[i:length(x)]-mean(x[i:length(x)]))^2)))/(-sum((x-mean(x))^2))
}
res
}
cusum_2 = function(x){
res = rep(0, length(x))
s_k = log_like_rat(x)
for(i in 1:length(x)){
res[i] = sum(s_k[1:i]) - min(s_k[1:i])
}
res
}
cusum_3 = function(x){
res = rep(0, length(x))
s_k = log_like_rat(x)
for(i in 1:length(x)){
res[i] = sum(s_k[1:i])
}
res
}
cusum_ratio = function(x){
res = rep(0, length(x))
res2 = rep(0, length(x))
s_k = log_like_rat(x)
for(i in 1:length(x)){
res[i] = sum(s_k[1:i])
res2[i] = res[i] - min(res)
}
res2
}
cusum_4 = function(x){
res = rep(0, length(x))
s_k = ratio2(x)
for(i in 1:length(x)){
res[i] = sum(s_k[1:i])
}
res
}
lnvar = function(x) {
var(log(x))
}
lnmean = function(x){
mean(log(x))
}
# compare distributions
lognormal = function(x) {
-(length(x)/2 * log(2*pi*lnvar(x)))-sum(log(x))-(sum(log(x)^2)/(2*lnvar(x)))+(sum(log(x)*lnmean(x))/lnvar(x))-((length(x)*lnmean(x))/(2*lnvar(x)))
}
lognormal_ratio = function(x) {
res = rep(0, length(x))
for(i in 1:length(x)){
res[i] = (L_lognormal(x[1:(i-1)]) * L_lognormal(x[i:length(x)]))/L_lognormal(x)
}
res
}
lnvar = function(x) {
var(log(x))
}
lnmean = function(x){
mean(log(x))
}
lognormal_2 = function(x) {
-(length(x)/2 * log(2*pi*1))-sum(log(x))-(sum(log(x)^2)/(2*1))+(sum(log(x)*lnmean(x))/1)-((length(x)*lnmean(x))/(2*1))
}
lognormal_ratio_2 = function(x) {
res = rep(0, length(x))
for(i in 1:length(x)){
res[i] = (L_lognormal_2(x[1:(i-1)]) * L_lognormal_2(x[i:length(x)]))/L_lognormal_2(x)
}
res
}
ratio_lognormal = function(x) {
x = x + 0.000000000000000001
res = rep(0, length(x))
for(i in 1:length(x)){
res[i] = -(sum((log(x[1:(i-1)])-lnmean(x[1:(i-1)]))^2) + sum((log(x[i:length(x)])-lnmean(x[i:length(x)]))^2))
}
res
}