In eikeluedeling/decisionSupport: Quantitative Support of Decision Making under Uncertainty

Example from Hubbard (2014), ch. 7, The value of information for ranges:

welfare function [ w_{PA}(x) = px - c ] $x$: units sold lutz

$P_x:$ Normal distribution with 90\%-confidence interval: $[c_l,c_u]:=[1.5 \cdot 10^5, 3.0 \cdot 10^5]$

$p$: unit price

$c$: campaign costs

library(decisionSupport)
n=100000

sales<-estimate("norm", 1.5e+05, 3.0e+05, variable="sales")
p<-25
c<-5e+06

profitModel<-function(x) {
  list(Profit = p*x$sales - c)
}
individualEvpiResult<-individualEvpiSimulation(welfare=profitModel,
                                               currentEstimate=sales,
                                               numberOfModelRuns=n,
                                               functionSyntax="data.frameNames")
# Show the simulation results:
print(sort(summary(individualEvpiResult),decreasing=TRUE,along="Profit"))

hist(individualEvpiResult, breaks=100)
hist(individualEvpiResult$current$mcResult$x$sales, breaks=100)

[ EL_{PA}=( c - p\mu) \Phi(\frac{1}{\sigma}(\frac{c}{p} - \mu)) + \frac{p\sigma^2 }{\sqrt{2 \pi}\sigma} e^{-\frac{1}{2 \sigma^2} (\frac{c}{p} - \mu)^2 } ] $\mu = \frac{c_l + c_u}{2}$

$\sigma = \frac{\mu - c_l}{\Phi^{-1}(0.95)}\approx \frac{c_u - c_l}{3.289707}$

mu<-(sales$marginal["sales","lower"] + sales$marginal["sales","upper"])/2
sigma<-(mu - sales$marginal["sales","lower"])/qnorm(0.95)

elPa_calc<-(c - p*mu)*pnorm( (c/p - mu)/sigma ) + p*sigma^2 * dnorm(x=c/p,mean=mu,sd=sigma)
print(elPa_calc)
elPa_sim<-individualEvpiResult$current$elPa[["Profit"]]
print(elPa_sim)
all.equal(elPa_calc, elPa_sim, tolerance=2/sqrt(n), scale=elPa_calc, use.names=FALSE)

eikeluedeling/decisionSupport documentation built on April 12, 2024, 7:25 a.m.