# Rproject6_LRTest_Poisson.r
# Example 8.4.A: Counts of asbestos fibers on filters
# Steel et al. 1980
# 1. Data ----
x=c(31,29,19,18,31,28,
34,27,34,30,16,18,
26,27,27,18,24,22,
28,24,21,17,24)
# x= rpois(n=100, lambda=24.91)
# 2. Parameter Estimation of Poisson----
# Suppose x is a sample of size n=23 from a Poisson(lambda) distribution
#
# 2.1 Estimate of lambda (MOM and MLE are the same)
lambda.hat=mean(x)
print(lambda.hat)
## [1] 24.91304
#
par(mfcol=c(1,1))
# 2.2 Plot histograms of sample data
# Vary argument nclass= for number of bins
hist(x, xlim=c(0,1.5*max(x)), probability=TRUE)
![](data:image/png;base64,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)
hist(x,nclass=15, xlim=c(0,1.5*max(x)), probability=TRUE)
![](data:image/png;base64,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)
hist(x,nclass=10, xlim=c(0,1.5*max(x)), probability=TRUE)
# Add plot of pmf function for fitted Poisson distribution
x.grid=seq(0,1.5*max(x),1)
x.probs=dpois(x.grid, lambda=lambda.hat)
lines(x.grid,x.probs, type="h", col='blue',lwd=4)
![](data:image/png;base64,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)
#
lambda.hat.sterror=sqrt(lambda.hat/length(x))
print(lambda.hat.sterror)
## [1] 1.040757
# 3. Likelihood Ratio Test Based on Histogram
nclass0=10
hist.0<-hist(x,nclass=nclass0)
![](data:image/png;base64,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)
print(hist.0$counts)
## [1] 5 1 2 3 1 5 2 2 2
n.bins=length(hist.0$counts)
print(hist.0$breaks)
## [1] 16 18 20 22 24 26 28 30 32 34
# cdf values at the breaks
hist.0.breaks.MLEFITTED.cdf=ppois(hist.0$breaks, lambda=lambda.hat)
# bin probabilities are the differences
hist.0.pbin=diff(hist.0.breaks.MLEFITTED.cdf)
####
# 3.1 Construct vectors of Observed and Expected counts
counts.Observed=hist.0$counts
probs.mle=hist.0.pbin
counts.sum=sum(counts.Observed)
counts.Expected=counts.sum*probs.mle
#labels.BloodType=c("M","MN","N")
# 3.2 Compute LRStat
# Conduct level alpha=0.05 test
# Compute P-Value
component.LRStat=2*counts.Observed*log(counts.Observed/counts.Expected)
LRStat=sum(component.LRStat)
print(LRStat)
## [1] 15.82175
#
# Under Null Hypothesis, LRStat is a chi-square r.v. with
# q=(m-1) -1 degrees of freedom
# where m=number of bins
# For level alpha test, determine critical value of LRStat
alpha=.05
m=n.bins
q=m-1-1
print(q)
## [1] 7
chisq.criticalValue=qchisq(p=1-alpha,df=q)
print(chisq.criticalValue)
## [1] 14.06714
# Test rejected at alpha level (LRStat > chisq.criticalValue)
#
# Compute P-value of LRStat
LRStat.pvalue=1-pchisq(LRStat, df=q)
print(LRStat.pvalue)
## [1] 0.02679569
# 4. Pearson ChiSquare Test ----
# 4.1 Construct vectors of Observed and Expected counts
counts.Observed=hist.0$counts
probs.mle=hist.0.pbin
counts.sum=sum(counts.Observed)
counts.Expected=counts.sum*probs.mle
# 4.2 Compute Pearson ChiSqStat
# Conduct level alpha=0.05 test
# Compute P-Value
component.ChiSqStat=((counts.Observed-counts.Expected)^2 )/counts.Expected
ChiSqStat=sum(component.ChiSqStat)
print(ChiSqStat)
## [1] 16.84007
#
# Under Null Hypothesis, LRStat is a chi-square r.v. with
# q=(m-1) -1 degrees of freedom
# where m=number of bins
# For level alpha test, determine critical value of LRStat
alpha=.05
m=n.bins
q=m-1-1
print(q)
## [1] 7
chisq.criticalValue=qchisq(p=1-alpha,df=q)
print(chisq.criticalValue)
## [1] 14.06714
# Test accepted at alpha level (ChiSqStat < chisq.criticalValue)
#
# Compute P-value of ChiSqStat
ChiSqStat.pvalue=1-pchisq(ChiSqStat, df=q)
print(ChiSqStat.pvalue)
## [1] 0.01845707
############################
# 5. Create Table for Both Tests ----
table.lrtests<-data.frame(
Observed=counts.Observed,
Expected=counts.Expected,
LRStat.j=component.LRStat,
ChiSqStat.j=component.ChiSqStat)
# Add last row equal to sums of columns
# Use r function apply(X=, MARGIN=, FUN=)
table.lrtests.0<-rbind(
table.lrtests,
t(as.matrix(apply(X=table.lrtests,MARGIN=2,FUN=sum))))
labels.tablerows<-paste("Bin_",c(1:n.bins),"[",
hist.0$breaks[1:(n.bins)],",",
hist.0$breaks[2:(n.bins+1)],"]",sep="")
dimnames(table.lrtests.0)[[1]]<-c(labels.tablerows,"Total/Sum")
print(table.lrtests.0)
## Observed Expected LRStat.j ChiSqStat.j
## Bin_1[16,18] 5 1.2812509 13.6160105 10.79343231
## Bin_2[18,20] 1 2.1902179 -1.5680021 0.64679349
## Bin_3[20,22] 2 3.0734068 -1.7185579 0.37489412
## Bin_4[22,24] 3 3.6030113 -1.0989460 0.10092185
## Bin_5[24,26] 1 3.5810485 -2.5513113 1.86029635
## Bin_6[26,28] 5 3.0554534 4.9250991 1.23754511
## Bin_7[28,30] 2 2.2621571 -0.4926865 0.03038089
## Bin_8[30,32] 2 1.4669015 1.2399793 0.19373762
## Bin_9[32,34] 2 0.8399652 3.4701678 1.60206703
## Total/Sum 23 21.3534126 15.8217528 16.84006878
print(data.frame(cbind(LRStat.pvalue=LRStat.pvalue,
ChiSqStat.pvalue=ChiSqStat.pvalue),
row.names=c("P-Value")))
## LRStat.pvalue ChiSqStat.pvalue
## P-Value 0.02679569 0.01845707