Expo~CDF
pEx = function(x,p)
{
p = 0.18848
pexp(x,p)
}
ks1=ad1=cvm1=NULL
ks1=ks.test(y,pEx)
ad1=ad.test(y,pEx)
cvm1=cvm.test(y,pEx)
result1=c(ks1$statistic,ks1$p.value,ad1$statistic,ad1$p.value,
cvm1$statistic,cvm1$p.value)
Appendix A.5. Graphics—To Plot the EPDF for the First Data Set
x = c(2.15, 2.20, 2.55, 2.56, 2.63, 2.74, 2.81, 2.90, 3.05, 3.41, 3.43,
3.43, 3.84, 4.16, 4.18, 4.36, 4.42, 4.51, 4.60, 4.61, 4.75, 5.03, 5.10,
5.44, 5.90, 5.96, 6.77, 7.82, 8.00, 8.16, 8.21, 8.72, 10.40, 13.20, 13.70)
hist(x,prob=T,main="Histogram and estimated PDFs",
col="pink", ylab = "PDF",ylim=c(0,0.05), bty ="n")
p = 0.14870 ## parameter estimate of S-ML model
```

```
curve(((pi/2)*(p/(1+p))*(exp(-2*p*x))*((1+p)*exp(p*x)+(2*x*p)-1)*
(sin((pi/2)*(1+exp(-p*x)*((x*p)/(1+p)))*exp(-x*p)))),col="blue",lwd=3,
add=T)
p = 0.22660 # parameter estimate of S-Lindley
curve(((pi/2)*((p^2)/(1+p))*(1+x)*exp(-p*x)*(sin((pi/2)*
(1+((x*p)/(1+p)))*exp(-x*p)))), col="green",lwd = 3, add=T)
p = 0.10780 # parameter estimate of S-Expo
curve(((pi/2)*(p*exp(-p*x))*(sin((pi/2)*exp(-x*p)))), col="orange",
lwd = 3, add=T)
p = 4.9096 # parameter estimate of IL
curve((((p^2)/(1+p))*((1+x)/x^3)*exp(-p/x)),col="red",lwd = 3, add=T)
p = 0.18848 # parameter estimate of Expo
curve(dexp(x,p), col="yellow", lwd = 3, add = T)
legend("topright",legend = c("S-ML","S-Lindley","S-Expo","IL","Expo"),
ncol = 1,
col= c("blue","green","orange","red","yellow"),lty =1,lwd=3,
text.width = 2.5 , inset= 0.00005, bty ="n")
Appendix A.6. Graphics—To Plot the ECDF for the First Data Set
 y = c(2.15, 2.20, 2.55, 2.56, 2.63, 2.74, 2.81, 2.90, 3.05, 3.41, 3.43,
 3.43, 3.84, 4.16, 4.18, 4.36, 4.42, 4.51, 4.60, 4.61, 4.75, 5.03, 5.10,
 5.44, 5.90, 5.96, 6.77, 7.82, 8.00, 8.16, 8.21, 8.72, 10.40, 13.20, 13.70)
plot(ecdf(y) , verticals=TRUE, main="Empirical and estimated CDFs",
 ylab="CDF", xlab="x", bty ="n")
p = 0.14870 # parameter estimate of S-ML
curve((cos((pi/2)*(1+(exp(-p*x)*((x*p)/(1+p))))*exp(-p*x))),col="blue",
lwd=3, add=T)
p = 0.22660 # parameter estimate of S-Lindley
curve((cos((pi/2)*(1+((x*p)/(1+p)))*exp(-p*x))), col="green",lwd = 3,
add=T)
p = 0.010780 # parameter estimate of S-Expo
curve((cos((pi/2)*exp(-p*x))),col="orange",lwd = 3, add=T)
p = 4.9096 # parameter estimate of IL
curve(((1 + (p/((1+p)*x)))*exp(-p/x)),col="red",lwd = 3, add=T)
p = 0.18848 # parameter estimate of Expo
curve(pexp(x,p), col="yellow", lwd = 3, add = T)
legend("topleft",legend = c("S-ML","S-Lindley","S-Expo","IL","Expo"),
ncol = 1,
col= c("blue","green","orange","red","yellow"),lty =1,lwd=3,
text.width = 2.5 , inset= 0.00005, bty ="n")
#######
```
*Appendix A.7. Graphics: Bar Plot and TTT Plot for First Data Set*

###Bar plot x = c(2.15, 2.20, 2.55, 2.56, 2.63, 2.74, 2.81, 2.90, 3.05, 3.41, 3.43, 3.43, 3.84, 4.16, 4.18, 4.36, 4.42, 4.51, 4.60, 4.61, 4.75, 5.03, 5.10, 5.44, 5.90, 5.96, 6.77, 7.82, 8.00, 8.16, 8.21, 8.72, 10.40, 13.20, 13.70) boxplot(x,main = "Tumour size of lung cancer patients", col = "orange", border="brown",horizontal = TRUE,notch = TRUE) ###TTT plot install.packages ("AdequacyModel") library(AdequacyModel) TTT(x, lwd = 2, lty 2, col = "red", grid=FALSE)
