DataXL - Blog

Welcome post

Sat, 01 Jan 2050 12:03:00 +0000

Across the world, the combined ratio is too high is not by chance that non-life companies face a profitability problem.

An insurance company has a production based on a 'raw material’, whose cost is not known at the time of the insurance. So, they use a lot of actuarial models to find this cost.

Then, insurance companies sum all the other expenses and put a margin on top. And they say they have a "price".

But… summing up all costs loadings only gives ‘the total cost’, not a price!

How should an insurance company define it’s price?

Our blog tells the story.

Find us at: http://dataxl.mozello.com/
Our archive is here.

Some R models about coronavirus

Thu, 26 Mar 2020 01:00:00 +0000

Dataset <- read.table("clipboard", header = TRUE, sep = "\t", na.strings = "NA",dec = ".", strip.white = TRUE)

## Dados da wikipedia.
# https://en.wikipedia.org/wiki/2020_coronavirus_pandemic_in_Italy
# https://en.wikipedia.org/wiki/2020_coronavirus_pandemic_in_Germany
# https://en.wikipedia.org/wiki/2020_coronavirus_pandemic_in_France
# https://en.wikipedia.org/wiki/2020_coronavirus_pandemic_in_Spain

library(Rcmdr)
library( "systemfit" )
library( MASS )

###################################
#BOX COX - teste ##
#-adequado para ver quando há abandono de exponencial (lambda >0 )
###################################

#https://stackoverflow.com/questions/33999512/how-to-use-the-box-cox-power-transformation-in-r

powerTransform <- function(y, lambda1, lambda2 = NULL, method = "boxcox") {

boxcoxTrans <- function(x, lam1, lam2 = NULL) {

    # if we set lambda2 to zero, it becomes the one parameter transformation
    lam2 <- ifelse(is.null(lam2), 0, lam2)

    if (lam1 == 0L) {
      log(y + lam2)
    } else {
      (((y + lam2)^lam1) - 1) / lam1
    }
}

switch(method
         , boxcox = boxcoxTrans(y, lambda1, lambda2)
         , tukey = y^lambda1
)
}

InversePowerTransform <- function(y, lam) {

      return( (y*lam+1)^(1/lam))

}

oldpar <- par(oma = c(0, 0, 3, 0), mfrow = c(2, 3))

IT<-boxcox((IT)~Dias, data=Dataset)
lambda.IT <- IT$x[which.max(IT$y)]
IT <- lm(powerTransform(IT, lambda.IT) ~ Dias,data=Dataset)
summary(IT)

GR<-boxcox((GR)~Dias, data=Dataset)
(lambda.GR <- GR$x[which.max(GR$y)])
GR <- lm(powerTransform(GR, lambda.GR) ~ Dias,data=Dataset)
summary(GR)

FR<-boxcox((FR)~Dias, data=Dataset)
(lambda.FR <- FR$x[which.max(FR$y)])
FR <- lm(powerTransform(FR, lambda.FR) ~ Dias,data=Dataset)
summary(FR)

SP<-boxcox((SP)~Dias, data=Dataset)
(lambda.SP <- SP$x[which.max(SP$y)])
SP <- lm(powerTransform(SP, lambda.SP) ~ Dias,data=Dataset)
summary(SP)

#PT<-boxcox((PT)~Dias, data=Dataset[20-7:20,])
PT<-boxcox((PT)~Dias, data=Dataset)
(lambda.PT <- PT$x[which.max(PT$y)])
PT <- lm(powerTransform(PT, lambda.PT) ~ Dias,data=Dataset)
summary(PT)

par(oldpar)

###################################
#MODELO BOX COX previsão (depende do modulo anterior para obtenção de Lambda)
###################################

IT <- lm(powerTransform(IT, lambda.IT) ~ Dias,data=Dataset)
GR <- lm(powerTransform(GR, lambda.GR) ~ Dias,data=Dataset)
FR <- lm(powerTransform(FR, lambda.FR) ~ Dias,data=Dataset)
SP <- lm(powerTransform(SP, lambda.SP) ~ Dias,data=Dataset)
PT <- lm(powerTransform(PT, lambda.PT) ~ Dias,data=Dataset)

summary(IT)
summary(GR)
summary(FR)
summary(SP)
summary(PT)

oldpar <- par(oma = c(0, 0, 3, 0), mfrow = c(2, 2))
plot(PT)
par(oldpar)
dev.off()

#previsão
Dataset$IT.pred.bc<-InversePowerTransform(predict(IT,newdata=Dataset),lambda.IT)
Dataset$GR.pred.bc<-InversePowerTransform(predict(GR,newdata=Dataset),lambda.GR)
Dataset$FR.pred.bc<-InversePowerTransform(predict(FR,newdata=Dataset),lambda.FR)
Dataset$SP.pred.bc<-InversePowerTransform(predict(SP,newdata=Dataset),lambda.SP)
Dataset$PT.pred.bc<-InversePowerTransform(predict(PT,newdata=Dataset),lambda.PT)

#32    30    27    30    24

Dataset$IT.dia33.CasosPorMilhão<-c(Dataset[1:32,]$IT,Dataset[33:106,]$IT.pred.bc)
Dataset$GR.dia30.CasosPorMilhão<-c(Dataset[1:30,]$GR,Dataset[31:106,]$GR.pred.bc)
Dataset$FR.dia27.CasosPorMilhão<-c(Dataset[1:27,]$FR,Dataset[28:106,]$FR.pred.bc)
Dataset$SP.dia30.CasosPorMilhão<-c(Dataset[1:30,]$SP,Dataset[31:106,]$SP.pred.bc)
Dataset$PT.dia24.CasosPorMilhão<-c(Dataset[1:24,]$PT,Dataset[25:106,]$PT.pred.bc)

oldpar <- par(oma = c(0, 0, 3, 0), mfrow = c(1, 3))
with(Dataset[1:24,], lineplot(Dias,
                              PT.dia24.CasosPorMilhão,
                              IT.dia33.CasosPorMilhão   ,
                              SP.dia30.CasosPorMilhão,
                              GR.dia30.CasosPorMilhão,
                              FR.dia27.CasosPorMilhão))

with(Dataset[1:35,], lineplot(Dias,
                              PT.dia24.CasosPorMilhão,
                              IT.dia33.CasosPorMilhão   ,
                              SP.dia30.CasosPorMilhão,
                              GR.dia30.CasosPorMilhão,
                              FR.dia27.CasosPorMilhão))

with(Dataset[1:50,], lineplot(Dias,
                              PT.dia24.CasosPorMilhão,
                              IT.dia33.CasosPorMilhão   ,
                              SP.dia30.CasosPorMilhão,
                              GR.dia30.CasosPorMilhão,
                              FR.dia27.CasosPorMilhão))
par(oldpar)
dev.off()

Dataset$IT.pred.bc.casos<-round(Dataset$IT.pred.bc*60461826/1000000,0)
Dataset$GR.pred.bc.casos<-round(Dataset$GR.pred.bc*83783942/1000000,0)
Dataset$FR.pred.bc.casos<-round(Dataset$FR.pred.bc*65273511/1000000,0)
Dataset$SP.pred.bc.casos<-round(Dataset$SP.pred.bc*46754778/1000000,0)
Dataset$PT.pred.bc.casos<-round(Dataset$PT.pred.bc*10196709/1000000,0)

Dataset$IT.casos<-round(Dataset$IT*60461826/1000000,0)
Dataset$GR.casos<-round(Dataset$GR*83783942/1000000,0)
Dataset$FR.casos<-round(Dataset$FR*65273511/1000000,0)
Dataset$SP.casos<-round(Dataset$SP*46754778/1000000,0)
Dataset$PT.casos<-round(Dataset$PT*10196709/1000000,0)

# Qualidade do modelo
oldpar <- par(oma = c(0, 0, 3, 0), mfrow = c(2, 3))

plot(Dataset[complete.cases(Dataset$IT),]$IT,Dataset[complete.cases(Dataset$IT),]$IT.pred.bc)
abline(0,1,col="red")

plot(Dataset[complete.cases(Dataset$GR),]$GR,Dataset[complete.cases(Dataset$GR),]$GR.pred.bc)
abline(0,1,col="red")

plot(Dataset[complete.cases(Dataset$FR),]$FR,Dataset[complete.cases(Dataset$FR),]$FR.pred.bc)
abline(0,1,col="red")

plot(Dataset[complete.cases(Dataset$SP),]$SP,Dataset[complete.cases(Dataset$SP),]$SP.pred.bc)
abline(0,1,col="red")

plot(Dataset[complete.cases(Dataset$PT),]$PT,Dataset[complete.cases(Dataset$PT),]$PT.pred.bc)
abline(0,1,col="red")

par(oldpar)
dev.off()

oldpar <- par(oma = c(0, 0, 3, 0), mfrow = c(2, 3))
with(Dataset, lineplot(Dias, PT, PT.pred.bc))
with(Dataset, lineplot(Dias, IT, IT.pred.bc))
with(Dataset, lineplot(Dias, SP, SP.pred.bc))
with(Dataset, lineplot(Dias, GR, GR.pred.bc))
with(Dataset, lineplot(Dias, FR, FR.pred.bc))
dev.off()

###################################
#LOG-LIN com pto de massa
###################################
IT<-lm(log(IT)~Dias, data=Dataset)
GR<-lm(log(GR)~Dias, data=Dataset)
FR<-lm(log(FR)~Dias, data=Dataset)
SP<-lm(log(SP)~Dias, data=Dataset)
PT<-lm(log(PT)~Dias, data=Dataset)

Dataset$IT.pred.lm<-exp(predict(IT,newdata=Dataset))
Dataset$GR.pred.lm<-exp(predict(GR,newdata=Dataset))
Dataset$FR.pred.lm<-exp(predict(FR,newdata=Dataset))
Dataset$SP.pred.lm<-exp(predict(SP,newdata=Dataset))
Dataset$PT.pred.lm<-exp(predict(PT,newdata=Dataset))

weqIT<-lm(Dataset$IT~Dataset$IT.pred.lm-1)
weqGR<-lm(Dataset$GR~Dataset$GR.pred.lm-1)
weqFR<-lm(Dataset$FR~Dataset$FR.pred.lm-1)
weqSP<-lm(Dataset$SP~Dataset$SP.pred.lm-1)
weqPT<-lm(Dataset$PT~Dataset$PT.pred.lm-1)

wIT<-summary(weqIT)$coef[1]
wGR<-summary(weqGR)$coef[1]
wFR<-summary(weqFR)$coef[1]
wSP<-summary(weqSP)$coef[1]
wPT<-summary(weqPT)$coef[1]

Dataset$IT.pred.lm<-wIT*Dataset$IT.pred.lm
Dataset$GR.pred.lm<-wGR*Dataset$GR.pred.lm
Dataset$FR.pred.lm<-wFR*Dataset$FR.pred.lm
Dataset$SP.pred.lm<-wSP*Dataset$SP.pred.lm
Dataset$PT.pred.lm<-wPT*Dataset$PT.pred.lm

#30.0    28.0    25.0    28.0    22.0

Dataset$IT.dia30.CasosPorMilhão<-c(Dataset[1:30,]$IT,Dataset[31:106,]$IT.pred.lm)
Dataset$GR.dia28.CasosPorMilhão<-c(Dataset[1:28,]$GR,Dataset[29:106,]$GR.pred.lm)
Dataset$FR.dia25.CasosPorMilhão<-c(Dataset[1:25,]$FR,Dataset[26:106,]$FR.pred.lm)
Dataset$SP.dia28.CasosPorMilhão<-c(Dataset[1:28,]$SP,Dataset[29:106,]$SP.pred.lm)
Dataset$PT.dia22.CasosPorMilhão<-c(Dataset[1:22,]$PT,Dataset[23:106,]$PT.pred.lm)

oldpar <- par(oma = c(0, 0, 3, 0), mfrow = c(1, 3))
with(Dataset[1:22,], lineplot(Dias,
                              PT.dia22.CasosPorMilhão,
                              IT.dia30.CasosPorMilhão   ,
                              SP.dia28.CasosPorMilhão,
                              GR.dia28.CasosPorMilhão,
                              FR.dia25.CasosPorMilhão))

with(Dataset[1:30,], lineplot(Dias,
                              PT.dia22.CasosPorMilhão,
                              IT.dia30.CasosPorMilhão   ,
                              SP.dia28.CasosPorMilhão,
                              GR.dia28.CasosPorMilhão,
                              FR.dia25.CasosPorMilhão))

with(Dataset[1:40,], lineplot(Dias,
                              PT.dia22.CasosPorMilhão,
                              IT.dia30.CasosPorMilhão   ,
                              SP.dia28.CasosPorMilhão,
                              GR.dia28.CasosPorMilhão,
                              FR.dia25.CasosPorMilhão))
par(oldpar)
dev.off()

Dataset$IT.pred.lm.casos<-round(Dataset$IT.pred.lm*60461826/1000000,0)
Dataset$GR.pred.lm.casos<-round(Dataset$GR.pred.lm*83783942/1000000,0)
Dataset$FR.pred.lm.casos<-round(Dataset$FR.pred.lm*65273511/1000000,0)
Dataset$SP.pred.lm.casos<-round(Dataset$SP.pred.lm*46754778/1000000,0)
Dataset$PT.pred.lm.casos<-round(Dataset$PT.pred.lm*10196709/1000000,0)

Dataset$IT.casos<-round(Dataset$IT*60461826/1000000,0)
Dataset$GR.casos<-round(Dataset$GR*83783942/1000000,0)
Dataset$FR.casos<-round(Dataset$FR*65273511/1000000,0)
Dataset$SP.casos<-round(Dataset$SP*46754778/1000000,0)
Dataset$PT.casos<-round(Dataset$PT*10196709/1000000,0)

#View(as.data.frame(cbind(Dataset$PT.casos,Dataset$PT.pred.lm.casos)))
#View(as.data.frame(cbind(Dataset$IT.casos,Dataset$IT.pred.lm.casos)))

#with(Dataset[1:31,], lineplot(Dias, IT, IT.pred.lm))

############################
#COMPARAÇÃO DE CRESCIMENTO DE PT E IR LOG LIN. Toda a amostra
# confirmar
############################
# oldpar <- par(oma = c(0, 0, 3, 0), mfrow = c(1, 2))
#
# nn<-sum(complete.cases(Dataset$PT))
#
# betas.exponencialPT<-rep(NA,(nn-7))
#
#
# for(ii in 7:nn){
#
# PT<-lm(log(PT)~Dias, data=Dataset[1:ii,])
#
# betas.exponencialPT[ii-7]<-summary(PT)$coef[2]
# }
#
# plot(seq(from=8,to=nn,by=1),betas.exponencialPT,
#      main = "PT:: Taxa de crescimento, usando todos os dados desde o dia 8 em diante",
#      xlab="Dia de crise",
#      ylab="beta da regressão: log(casos permilhao)=constante +B * Dias",
#      type = "o",col="red",
#      )
#
#
#
# nn<-sum(complete.cases(Dataset$IT))
#
# betas.exponencialIT<-rep(NA,(nn-7))
#
#
# for(ii in 7:nn){
#
#   IT<-lm(log(IT)~Dias, data=Dataset[1:ii,])
#
#   betas.exponencialIT[ii-7]<-summary(IT)$coef[2]
# }
#
# plot(seq(from=8,to=nn,by=1),betas.exponencialIT,
#      main = "IT:: Taxa de crescimento, usando todos os dados desde o dia 8 em diante",
#      xlab="Dia de crise",
#      ylab="beta da regressão: log(casos permilhao)=constante +B * Dias",
#      type = "o",col="red",
# )
#
#
# par(oldpar)
#
#
# dias<-seq(from=8,to=sum(complete.cases(Dataset$IT)),by=1)
# betas.exponencialPT<-
#   c(betas.exponencialPT,
#     rep(NA,
#                   sum(complete.cases(Dataset$IT))
#                  -sum(complete.cases(Dataset$PT))
#                  )
#     )
#
# betas.exponencialIT<-betas.exponencialIT
#
# aux<-as.data.frame(cbind(dias,betas.exponencialPT,betas.exponencialIT))
#
# with(dias, lineplot(aux, betas.exponencialIT, betas.exponencialPT))
#
#

############################
#comparar taxa de crescimento PT vs IT
############################
nn<-sum(complete.cases(Dataset$PT))
betas.exponencialPT<-rep(NA,(nn-7))
for(ii in 8:nn){
aa=ii-7
PT<-lm(log(PT)~Dias, data=Dataset[aa:ii,])
betas.exponencialPT[ii-7]<-summary(PT)$coef[2]}

nn<-sum(complete.cases(Dataset$IT))
betas.exponencialIT<-rep(NA,(nn-7))
for(ii in 8:nn){
aa=ii-7
IT<-lm(log(IT)~Dias, data=Dataset[aa:ii,])
betas.exponencialIT[ii-7]<-summary(IT)$coef[2]}

dias<-seq(from=8,to=sum(complete.cases(Dataset$IT)),by=1)

betas.exponencialPT<-
c(betas.exponencialPT,
    rep(NA,
        sum(complete.cases(Dataset$IT))-sum(complete.cases(Dataset$PT))
    )
)

betas.exponencialIT<-betas.exponencialIT

aux<-as.data.frame(cbind(dias,betas.exponencialPT,betas.exponencialIT))

with(aux, lineplot(dias, betas.exponencialPT,betas.exponencialIT))
dev.off()

library(rio)
write.csv(Dataset,"C:\\Lixo\\Dataset.xls")

############################
#Qualidade do modelo log lin com massa
############################
oldpar <- par(oma = c(0, 0, 3, 0), mfrow = c(2, 3))

plot(Dataset[complete.cases(Dataset$IT),]$IT,Dataset[complete.cases(Dataset$IT),]$IT.pred.lm)
abline(0,1,col="red")

plot(Dataset[complete.cases(Dataset$GR),]$GR,Dataset[complete.cases(Dataset$GR),]$GR.pred.lm)
abline(0,1,col="red")

plot(Dataset[complete.cases(Dataset$FR),]$FR,Dataset[complete.cases(Dataset$FR),]$FR.pred.lm)
abline(0,1,col="red")

plot(Dataset[complete.cases(Dataset$SP),]$SP,Dataset[complete.cases(Dataset$SP),]$SP.pred.lm)
abline(0,1,col="red")

plot(Dataset[complete.cases(Dataset$PT),]$PT,Dataset[complete.cases(Dataset$PT),]$PT.pred.lm)
abline(0,1,col="red")

par(oldpar)
############################
#logistic.dxl - 100%
# não usar - talvez para Holanda e UK
# apenas meio feito
############################
#
#
# logistic.dxl <- function(p,x,unidade) {
#
#   p<-(p)/unidade
#   odds<-p/((1-p))
#   log.odds<-log(odds)
#   df<-as.data.frame(x)
#   aux1<-lm(log.odds~x)
#   log.odds.pred<-predict.lm(aux1,newdata=df)
#   odds.pred<-exp(log.odds.pred)
#   p.pred<-odds.pred/(1+odds.pred)
#
#   return(p.pred*unidade)
# }
#
# IT<-logistic.dxl(Dataset$IT,Dataset$Dias,1000000)
# GR<-logistic.dxl(Dataset$GR,Dataset$Dias,1000000)
# FR<-logistic.dxl(Dataset$FR,Dataset$Dias,1000000)
# SP<-logistic.dxl(Dataset$SP,Dataset$Dias,1000000)
# PT<-logistic.dxl(Dataset$PT,Dataset$Dias,1000000)
#
#
# lineplot(Dataset$Dias,PT,IT,GR,FR,SP)
#
# max(PT)

############################
#logistic 2
############################

library("drc")
#https://stackoverflow.com/questions/43562591/r-fit-logistic-curve-through-a-scatterplot/43564372
#https://rstats4ag.org/dose-response-curves.html
#https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4696819/

IT.log <- drm(IT ~ Dias, data = Dataset, fct = L.3(), type = "continuous") #para log-logistica colocar LL
GR.log <- drm(GR ~ Dias, data = Dataset, fct = L.3(), type = "continuous") #para log-logistica colocar LL
FR.log <- drm(FR ~ Dias, data = Dataset, fct = L.3(), type = "continuous") #para log-logistica colocar LL
SP.log <- drm(SP ~ Dias, data = Dataset, fct = L.3(), type = "continuous") #para log-logistica colocar LL
PT.log <- drm(PT ~ Dias, data = Dataset, fct = L.3(), type = "continuous") #para log-logistica colocar LL

dias.de.crise.em.pt<-sum(complete.cases(Dataset$PT))
dias.de.crise.em.pt.1<-dias.de.crise.em.pt-1
dias.de.crise.em.pt.2<-dias.de.crise.em.pt-2
PT.log1 <- drm(PT ~ Dias, data = Dataset[1:dias.de.crise.em.pt.1,], fct = L.3(), type = "continuous") #para log-logistica colocar LL
PT.log2 <- drm(PT ~ Dias, data = Dataset[1:dias.de.crise.em.pt.2,], fct = L.3(), type = "continuous") #para log-logistica colocar LL

#confirmar
logistic.dxl<-function(x, b,c, d, e){#L.3 na eq acima
return(c+
           (d-c)/((1+exp(
             b*(
               (x)-(e)
             )
           )
           ))
)
}

log.logistic.dxl<-function(x, b,c, d, e){#LL.3 na eq acima
return(c+
           (d-c)/((1+exp(
             b*(
               log(x)-log(e)
             )
           )
           ))
)
}

Dataset$IT.pred.log<-(predict(IT.log,newdata = Dataset))
Dataset$GR.pred.log<-(predict(GR.log,newdata = Dataset))
Dataset$FR.pred.log<-(predict(FR.log,newdata = Dataset))
Dataset$SP.pred.log<-(predict(SP.log,newdata = Dataset))
Dataset$PT.pred.log<-(predict(PT.log,newdata = Dataset))
Dataset$PT.pred.log1<-(predict(PT.log1,newdata = Dataset))
Dataset$PT.pred.log2<-(predict(PT.log2,newdata = Dataset))

xxxx<-(log.logistic.dxl(Dataset$Dias,
                        summary(PT.log)$coef[1],
                        0,
                        summary(PT.log)$coef[2],
                        summary(PT.log)$coef[3]))
#plot(xxxx)

yyyy<-(logistic.dxl(Dataset$Dias,
                    summary(PT.log)$coef[1],
                    0,
                    summary(PT.log)$coef[2],
                    summary(PT.log)$coef[3]))

dev.off()
plot(Dataset$PT.pred.log,yyyy)
abline(0,1)

Dataset$IT.pred.log.casos<-round(Dataset$IT.pred.log*60461826/1000000,0)
Dataset$GR.pred.log.casos<-round(Dataset$GR.pred.log*83783942/1000000,0)
Dataset$FR.pred.log.casos<-round(Dataset$FR.pred.log*65273511/1000000,0)
Dataset$SP.pred.log.casos<-round(Dataset$SP.pred.log*46754778/1000000,0)
Dataset$PT.pred.log.casos<-round(Dataset$PT.pred.log*10196709/1000000,0)

dev.off()
oldpar <- par(oma = c(0, 0, 3, 0), mfrow = c(2, 3))
with(Dataset[1:50,], lineplot(Dias, IT, IT.pred.log))
with(Dataset[1:50,], lineplot(Dias, GR, GR.pred.log))
with(Dataset[1:50,], lineplot(Dias, FR, FR.pred.log))
with(Dataset[1:50,], lineplot(Dias, SP, SP.pred.log))
with(Dataset[1:50,], lineplot(Dias, PT, PT.pred.log))

with(Dataset[1:50,], lineplot(Dias
                              ,PT.pred.log
                              ,IT.pred.log
                              ,SP.pred.log
                              ,GR.pred.log
                              ,FR.pred.log
))

par(oldpar)

horizonte=40
temp.decorrido=24

plot (Dataset[1:horizonte,]$Dias,Dataset[1:horizonte,]$PT.pred.log,ylim=c(0,2500),xlab="dias de crise",ylab="casos por milhão", col="black", type="b")
lines(Dataset[1:horizonte,]$Dias,Dataset[1:horizonte,]$SP.pred.log,col="orange", type="b")
lines(Dataset[1:horizonte,]$Dias,Dataset[1:horizonte,]$GR.pred.log,col="red", type="b")
lines(Dataset[1:horizonte,]$Dias,Dataset[1:horizonte,]$IT.pred.log,col="green", type="b")
lines(Dataset[1:horizonte,]$Dias,Dataset[1:horizonte,]$FR.pred.log,col="blue", type="b")
legend(1, 2400, legend=c("Portugal", "Espanha","Alemanha","Itália","França"),
       col=c("black", "orange", "red", "green","blue"), lty=1:2, cex=0.8)

plot (Dataset[1:horizonte,]$Dias,Dataset[1:horizonte,]$PT.pred.log,ylim=c(0,800),xlab="dias de crise",ylab="casos por milhão", col="black", type="b")
lines(Dataset[1:horizonte,]$Dias,Dataset[1:horizonte,]$PT.pred.log1,col="red", type="b")
lines(Dataset[1:horizonte,]$Dias,Dataset[1:horizonte,]$PT.pred.log2,col="blue", type="b")
abline(v=dias.de.crise.em.pt, col="grey")
legend(1, 750, legend=c("Portugal - previsão ao dia de hoje", "Portugal - previsão ao dia de ontem",
                        "Portugal - previsão ao dia de anteontem",
                        paste0("Dia de crise (hoje): ",dias.de.crise.em.pt,".º")),
       col=c("black", "red", "blue","grey"), lty=1:2, cex=0.8)

Dataset$D.PT.pred.log <- c(NA,diff(Dataset$PT.pred.log,differences = 1))
Dataset$D.PT.pred.log.casos <- c(NA,diff(Dataset$PT.pred.log.casos,differences = 1))

dev.off()
with(Dataset[1:50,], lineplot(Dias
                              ,PT
                              ,PT.pred.log
                              ,D.PT.pred.log
))

dev.off()
horizonte=40
temp.decorrido=23
max<-Dataset$Dias[which.max(Dataset$D.PT.pred.log.casos)]

plot(x = Dataset[1:horizonte,]$Dias, y = Dataset[1:horizonte,]$PT.pred.log.casos, col="blue",ylab="N.º de casos",xlab="Dias desde o início da crise",type="l")
lines(x = Dataset[1:temp.decorrido,]$Dias, y = Dataset[1:temp.decorrido,]$PT.casos,type="p")
lines(x = Dataset[1:horizonte,]$Dias, y = Dataset[1:horizonte,]$D.PT.pred.log.casos, col="red")
abline(a=NULL, b=NULL, h=NULL, v=temp.decorrido, col="grey")
#abline(a=NULL, b=NULL, h=NULL, v=max, col="dark grey")
legend(1, 6000, legend=c("Portugal - evolução prevista (ao dia de hoje) para o total de casos (acumulado)"
                         ,"Portugal - evolução real do total de casos (acumulado)"
                         ,"Portugal - evolução de novos casos"
                         ,paste0("Dia de crise (hoje): ",dias.de.crise.em.pt,".º")
                         #,paste0("Pico de novos casos")
                        ),
       col=c("black"
             ,"red"
             ,"blue"
             ,"grey"
             #,"dark grey"
             ), lty=1:2, cex=0.8)

# oldpar <- par(oma = c(0, 0, 3, 0), mfrow = c(2, 3))
# with(Dataset, lineplot(Dias, IT.casos, IT.pred.log.casos))
# #with(Dataset, lineplot(Dias, GR.casos, GR.pred.log.casos))
# with(Dataset, lineplot(Dias, FR.casos, FR.pred.log.casos))
# with(Dataset, lineplot(Dias, SP.casos, SP.pred.log.casos))
# with(Dataset, lineplot(Dias, PT.casos, PT.pred.log.casos))
#
# with(Dataset, lineplot(Dias,
#                        PT.pred.log.casos,
#                        IT.pred.log.casos,
#                        SP.pred.log.casos,
#                        GR.pred.log.casos,
#                        FR.pred.log.casos
#                       )
#                       )
#
# par(oldpar)

max(Dataset$IT.pred.log.casos)/1000
max(Dataset$GR.pred.log.casos)/1000
max(Dataset$FR.pred.log.casos)/1000
max(Dataset$SP.pred.log.casos)/1000
max(Dataset$PT.pred.log.casos)/1000

export(Dataset,"C:/lixo/Dataset.xlsx")

############################
#SUR - LIXO
############################
# ####
# IT<-(log(IT)~+Dias)
# GR<-(log(GR)~Dias)
# FR<-(log(FR)~Dias)
# SP<-(log(SP)~Dias)
# PT<-(log(PT)~Dias)
#
# IT <- (powerTransform(IT, lambda.IT) ~ Dias)
# GR <- (powerTransform(GR, lambda.GR) ~ Dias)
# FR <- (powerTransform(FR, lambda.FR) ~ Dias)
# SP <- (powerTransform(SP, lambda.SP) ~ Dias)
# PT <- (powerTransform(PT, lambda.PT) ~ Dias)
#
# eqSystem <- list(IT   ,GR,   FR,   SP,   PT)
# sur<-systemfit( eqSystem, method = "SUR", data = Dataset )
#
# summary(sur)
#
# sur.col<-(predict(sur,dataset=Dataset))
# names(sur.col)<-c("IT.pred",   "GR.pred",   "FR.pred",   "SP.pred",   "PT.pred")
#
# #Dataset$IT.pred.SUR<-exp(sur.col$IT.pred)
# #Dataset$GR.pred.SUR<-exp(sur.col$GR.pred)
# #Dataset$FR.pred.SUR<-exp(sur.col$FR.pred)
# #Dataset$SP.pred.SUR<-exp(sur.col$SP.pred)
# #Dataset$PT.pred.SUR<-exp(sur.col$PT.pred)
#
# Dataset$IT.pred.SUR<-InversePowerTransform(sur.col$IT.pred,lambda.IT)
# Dataset$GR.pred.SUR<-InversePowerTransform(sur.col$GR.pred,lambda.GR)
# Dataset$FR.pred.SUR<-InversePowerTransform(sur.col$FR.pred,lambda.FR)
# Dataset$SP.pred.SUR<-InversePowerTransform(sur.col$SP.pred,lambda.SP)
# Dataset$PT.pred.SUR<-InversePowerTransform(sur.col$PT.pred,lambda.PT)
#
#
# names(Dataset)
#
# weqIT<-lm(Dataset$IT~Dataset$IT.pred.SUR-1)
# weqGR<-lm(Dataset$GR~Dataset$GR.pred.SUR-1)
# weqFR<-lm(Dataset$FR~Dataset$FR.pred.SUR-1)
# weqSP<-lm(Dataset$SP~Dataset$SP.pred.SUR-1)
# weqPT<-lm(Dataset$PT~Dataset$PT.pred.SUR-1)
#
# wIT<-summary(weqIT)$coef[1]
# wGR<-summary(weqGR)$coef[1]
# wFR<-summary(weqFR)$coef[1]
# wSP<-summary(weqSP)$coef[1]
# wPT<-summary(weqPT)$coef[1]
#
#
# Dataset$IT.pred<-wIT*Dataset$IT.pred.SUR
# Dataset$GR.pred<-wGR*Dataset$GR.pred.SUR
# Dataset$FR.pred<-wFR*Dataset$FR.pred.SUR
# Dataset$SP.pred<-wSP*Dataset$SP.pred.SUR
# Dataset$PT.pred<-wPT*Dataset$PT.pred.SUR
#
#
# oldpar <- par(oma = c(0, 0, 3, 0), mfrow = c(2, 3))
#
# plot(Dataset$IT,Dataset$IT.pred.SUR)
# abline(0,1,col="red")
#
# plot(Dataset$GR,Dataset$GR.pred.SUR)
# abline(0,1,col="red")
#
# plot(Dataset$FR,Dataset$FR.pred.SUR)
# abline(0,1,col="red")
#
# plot(Dataset$SP,Dataset$SP.pred.SUR)
# abline(0,1,col="red")
#
# plot(Dataset$PT,Dataset$PT.pred.SUR)
# abline(0,1,col="red")
#
# par(oldpar)
#
#
# with(Dataset, lineplot(Dias, PT, PT.pred))
# with(Dataset, lineplot(Dias, IT, IT.pred))

PwC Scale #InsurTech programme - executive evening

Thu, 27 Jun 2019 13:09:00 +0000

It was great to be part of the PwC UK Scale Programme over the past 11 weeks.

Yesterday was the big event!

We presented our " optimization tool" & our "Suppliers Detection tool".

Check the fotos

Scale | InsurTech

Tue, 28 May 2019 22:56:00 +0000

Data XL is now a part of PwC scale program!

Here is our pitch! (check the slide presentation: https://www.slideshare.net/secret/wanFXlFN08JJQC)

***

Hi everyone
My name is Filipe Charters, and I’m the CEO of Data XL
We love the insurance sector; we believe that insurance companies have much to give to the world
Our business model is to provide tools - essentially insurance pricing tools – that make insures rock.
Today we bring to you our two flagship products.
. SUPPLIER OVERCHARGE DETECTION – a special case of fraud.
. Price optimization with an API
An optimal price is a price that optimizes the margin, the revenue OR minimizes the churn.
Insures companies define price in the following way:

(SLIDE)
. They sum all costs, and they say they a price. When you sum all costs, you have the total cost.
. insurers put the price near the cost, we want to put the price near the value.
This is why an IPHONE costs twice as much as a Samsung, even though the raw material is the same.

(SLIDE)
So, we build this platform, where insurance companies can put all their renewals information and receive the optimal price back.
The same input with same extra columns:
-    The price that max the revenue
-    The price that max the margin
-    The price that minimizes the churn
This platform is working now. It’s secure – it’s cloud base in a world class provider (digital ocean), but it can be stuck in your servers.
We do not define the strategy!! So, I cannot talk about the financials, but we can imagine what would mean for a price increase of 1%, maintain the same renewal rate.
As to accuracy we can say that our margin of error was more or less 2 %.
Just 2%.

(SLIDE)
Why are we different?
To make this happen we need:
. the risk numbers (which insures already have), the price of the competition and the will 2 pay model.
We developed some algorithms where we can reverse engineer the price of the competition.
And with very good experimental design we measure the will to pay.

No current provider offers this at the same time.
Also, our competitors offer a software and a manual.
Not a solution.

(SLIDE)
Are we compliance with the FSA for a transparent price?
. YES. We work with segments, so each policyholder with the same characteristics will receive the same price.
. We are fair, but efficient. If you need to lower your price, we can say how much lower should your price quote be.
If you want to charge more, we can say the optimal price.

(SLIDE)
Now let’s talk about abuse.
We are running out of time, let me be efficient.

The current anti-fraud procedure is: look to the surroundings around a claim.
We look to the provider. The health provider. The car repair shop.
Imagine that a maternity hospital makes a lot of c-section. Each and everyone can have the proper patter and medical justification.
But the overall expense will be higher, but above all the digit distribution in the expense will be different.

Imagine that a provider needs clinical authorization for expenses above 2000 pounds.
Whenever a doctor wants to make this specific procedure, he will split the expenses in two invoices.
With our algorithm we will be able to detect this overcharge, since we will analyse the digits that compose each invoice.
And what we're going to see that we have more expenses started with the digit “1 " than we would expect

(SLIDE)
You see, there is a statistical law for the leading digits.
We know that the digit 1 will appear as a leading digit in 30% of the time. As the digit 9, for example, will appear less than 5% as a leading digit.

(SLIDE)
We can take this a step further and check if the digits follow the right distribution.
For instances in this example we check the first two digits of every invoice follow the proper distribution (is the red line).
And we can see that expenses that there are too many invoices that starts with “2 and a 5”

(SLIDE)
As a result, we have a 66% accuracy of finding overcharge on providers-

(SLIDE)
We are making money with these two products
We have credentials that we can share.
Came talk to us
Let’s run a pilot

A marca "Data XL" é nossa!

Mon, 01 Apr 2019 16:00:00 +0000

Mais uma breve conquista! burocrática, é certo - mas sabe bem na mesma!

«Big Data Is A Sham» - a must read

Fri, 27 Apr 2018 16:18:00 +0000

«In sense from a mathematical, an ethical, stead of mining the behaviors of millions, we can get better insights from asking a few hundred, or a couple of thousand people about the things they’d like us to do. It makes betterand a creative point of view.» .

Check the full article here.

POR OS NÚMEROS NO CENTRO DA COMPANHIA

Wed, 11 Apr 2018 01:34:00 +0000

No meio de legislação e normas, há às vezes algumas supresas: "Tenho a certeza que as seguradoras sabem que têm de ser mais do que uma commodity: o desafio está em como o ser..." - o meu artigo na newsletter da APS

VER AQUI

The other side of the coin....

Mon, 05 Mar 2018 16:34:00 +0000

Sometimes (most of the time), clients surprise us.
- "I want to optimize my price!"
- "Sure!, More revenue, more margin, more policies - what is your goal?"
- "Minimize the cost, subject to this renewal share"
Minimize cost! Yes! So obvious now!

Photo credits: By Andrè Bellingrodt - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=39375494

Proudly presenting Lazarus - our new product for winning-back former customers

Mon, 29 Jan 2018 12:02:00 +0000

Proudly presenting Lazarus - our new product for winning-back former customers.
Check out our business case simulator and let us know what you think!
*
You know that the client has left the company.
You know that it's necessary to present a lower price.
But how low should the price be?

Data XL allows insurers to setup the win-back price!

Brouchure here.
Business case simulater here.

Demo day - Pitch :: Dec - 2017

Wed, 13 Dec 2017 17:24:00 +0000

Our pitch for @F10_accelerator at #F10Demo: insurance pricing optimization!

HERE