When I looked at the fits of the 6 global basins for annual Category 4 and 5 hurricane counts (Cat45) to a Poisson distribution using the goodfit function in R, I was surprised that the fits did have larger p values (better fit). When I did Monte Carlo simulations for random Poisson distributions with a lambda value approximating the lambda of the basin Cat45 counts, I also obtained low p values. After consultation with RomanM I found that the binning for the good fit function does not account for the end bins with low counts (less than the prescribed 5).

I redid my Poisson fits for Cat45 counts from the IBTracs data series using the 10 minute observed maximum wind speed converted to 1 minute using the factor 1.13 and average maximum wind speed of the sources used by IBTracs. The period was from 1984-2007 – as this is the period that has the most consistent observational criteria.

I simulated 10,000 Poisson distributions for lambdas approximating the lambdas from the basin Cat45 counts and obtained a distribution of p values for the fit of the distributions to a Poisson distribution. Before the simulations I determined the optimum binning strategy that would give the largest number of bins with at least 5 counts in a bin. I then used that binning for the Cat45 counts for the 6 basins and determine the p values for a Poisson fit.

I have listed the generic R code below and a table with a summary of the results. The table shows the basins, Western Pacific (WP), Eastern Pacific (EP), North Atlantic (NATL), South Pacific (SP), South Indian (SI) and North Indian (NI); the p values for the Poisson fit (p) and the percentage of simulated distributions with a lambda approximating that of the basin that had p values less than that calculated for the basins (%D). I guess, in order to avoid a “too good to be true” result, I would have preferred those fits to be closer to a 50% of the distribution.

Seeing all these basins with these levels of apparent fit to a Poisson for CAT counts leads me to conclude that these hurricanes result primarily from a random gathering of conditions and cannot be associated strongly with SST. I suspect that a next logical step would be to do a Poisson model that includes possible factors such as SST and wind fields, but at this point I do not see how the fits would improve.

]]>library(vcd)

z=rep(10000,0)

for (i in 1:10000){

X=rpois(n=24,lambda=3.5)

Xtab=table(factor(X,0:10))

ObX=as.numeric(Xtab)

Xo=c(sum(ObX[1:3]),sum(ObX[4:5]),sum(ObX[6:11]))

gfX=goodfit(X, type=”poisson”,method=”ML”)

Lambda=gfX$par

L=as.numeric(Lambda)

Exp=dpois(c(0,1:10),L)

Xe=c(sum(Exp[1:3]),sum(Exp[4:5]),1-sum(Exp[1:5]))

z[i]=chisq.test(Xo,p=Xe)$p.value}

hisz=hist(z,breaks=20,plot=FALSE)EP=read.csv(“WP”,skip=1)

EPmax=aggregate(EP[,13],by=list(Year=EP[,2],Number=EP[,3]),FUN=max)

EPcat=ifelse(EPmax[,3]>100,no=”No”,yes=ifelse(EPmax[,1]>1980,yes=”Cat45″,no=”No”))

EPcat2=cbind(EPcat,EPmax[,1])

Cat45=EPcat2[EPcat2[,1]==”Cat45″,]

X=as.numeric(Cat45[,2])

EP45=hist(X,breaks=1980:2008,plot=FALSE,)

EPct81_07=EP45$counts[1:27]

EPct84_07=EPct81_07[4:27]

X=EPct84_07

Xtab= table(factor(X,0:10))

ObX=as.numeric(Xtab)

Xo=c(sum(ObX[1:3]),sum(ObX[4:5]),sum(ObX[6:11]))

library(vcd)

gfX=goodfit(X, type=”poisson”,method=”ML”)

Lambda=gfX$par

L=as.numeric(Lambda)

Exp=dpois(c(0,1:10),L)

Xe=c(sum(Exp[1:3]),sum(Exp[4:5]),1-sum(Exp[1:5]))

chisq.test(Xo,p=c(Xe))$p.value

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