# \donttest{
###Univariate distributions example:
set.seed(1000)
junk<-rweibull(300,3,2)
##A faster ML estimtion
junk.fit1<-fun.RMFMKL.ml.m(junk)
junk.fit2<-fun.RPRS.ml.m(junk)
qqplot.gld(junk.fit1,data=junk,param="fmkl")
qqplot.gld(junk.fit2,data=junk,param="rs")
##Using discretised approach, with 50 classes
#Using discretised method with weights
obj.fit1.hs<-fun.data.fit.hs(junk)
#Plot the resulting fit. The fun.plot.fit function also works for singular fits
#such as those by fun.plot.fit(obj.fit1.ml,junk,nclass=50,
#param=c("rs","fmkl","fmkl"),xlab="x")
fun.plot.fit(obj.fit1.hs,junk,nclass=50,param=c("rs","fmkl"),xlab="x")
#Compare the mean, variance, skewness and kurtosis of the fitted distribution
#with actual data
fun.theo.mv.gld(obj.fit1.hs[1,1],obj.fit1.hs[2,1],obj.fit1.hs[3,1],
obj.fit1.hs[4,1],param="rs")
fun.theo.mv.gld(obj.fit1.hs[1,2],obj.fit1.hs[2,2],obj.fit1.hs[3,2],
obj.fit1.hs[4,2],param="fmkl")
fun.moments.r(junk)
#Conduct resample KS tests
fun.diag.ks.g(obj.fit1.hs[,1],junk,param="rs")
fun.diag.ks.g(obj.fit1.hs[,2],junk,param="fmkl")
##Try another fit, say 15 classes
obj.fit2.hs<-fun.data.fit.hs(junk,rs.default="N",fmkl.default="N",no.c.rs = 15,
no.c.fmkl = 15)
fun.plot.fit(obj.fit2.hs,junk,nclass=50,param=c("rs","fmkl"),xlab="x")
fun.theo.mv.gld(obj.fit2.hs[1,1],obj.fit2.hs[2,1],obj.fit2.hs[3,1],
obj.fit2.hs[4,1],param="rs")
fun.theo.mv.gld(obj.fit2.hs[1,2],obj.fit2.hs[2,2],obj.fit2.hs[3,2],
obj.fit2.hs[4,2],param="fmkl")
fun.moments.r(junk)
fun.diag.ks.g(obj.fit2.hs[,1],junk,param="rs")
fun.diag.ks.g(obj.fit2.hs[,2],junk,param="fmkl")
##Uses the maximum likelihood estimation method
#Fit the function using fun.data.fit.ml
obj.fit1.ml<-fun.data.fit.ml(junk)
#Plot the resulting fit
fun.plot.fit(obj.fit1.ml,junk,nclass=50,param=c("rs","fmkl","fmkl"),xlab="x",
name=".ML")
#Compare the mean, variance, skewness and kurtosis of the fitted distribution
#with actual data
fun.comp.moments.ml(obj.fit1.ml,junk)
#Do a quantile plot
qqplot.gld(junk,obj.fit1.ml[,1],param="rs",name="RS ML fit")
#Run a KS resample test on the resulting fit
fun.diag2(obj.fit1.ml,junk,1000)
#It is possible to use say fun.data.fit.ml(junk,rs.leap=409,fmkl.leap=409,
#FUN="QUnif") to find solution under a different set of low discrepancy number
#generators.
###Bimodal distributions example:
#Fitting mixture of generalised lambda distributions on the data set using both
#the maximum likelihood and partition maximum likelihood and plot the resulting
#fits
opar <- par()
par(mfrow=c(2,1))
junk<-fun.auto.bimodal.ml(faithful[,1],per.of.mix=0.01,clustering.m=clara,
init1.sel="rprs",init2.sel="rmfmkl",init1=c(-1.5,1.5),init2=c(-0.25,1.5),
leap1=3,leap2=3)
fun.plot.fit.bm(nclass=50,fit.obj=junk,data=faithful[,1],
name="Maximum likelihood using",xlab="faithful1",param.vec=c("rs","fmkl"))
#Do a quantile plot
qqplot.gld.bi(faithful[,1],junk$par,param1="rs",param2="fmkl",
name="RS FMKL ML fit",range=c(0.001,0.999))
par(opar)
junk<-fun.auto.bimodal.pml(faithful[,1],clustering.m=clara,init1.sel="rprs",
init2.sel="rmfmkl",init1=c(-1.5,1.5),init2=c(-0.25,1.5),leap1=3,leap2=3)
fun.plot.fit.bm(nclass=50,fit.obj=junk,data=faithful[,1],
name="Partition maximum likelihood using",xlab="faithful1",
param.vec=c("rs","fmkl"))
#Fit the faithful[,1] data from the dataset library using sobol sequence
#generator for the first distribution fit and halton sequence for the second
#distribution fit.
fit1<-fun.auto.bimodal.ml(faithful[,1],init1.sel="rmfmkl",init2.sel="rmfmkl",
init1=c(-0.25,1.5),init2=c(-0.25,1.5),leap1=3,leap2=3,fun1="runif.sobol",
fun2="runif.halton")
#Run diagnostic KS tests
fun.diag.ks.g.bimodal(fit1$par[1:4],fit1$par[5:8],prop1=fit1$par[9],
data=faithful[,1],param1="fmkl",param2="fmkl")
#Find the theoretical moments of the fit
fun.theo.bi.mv.gld(fit1$par[1],fit1$par[2],fit1$par[3],fit1$par[4],"fmkl",
fit1$par[5],fit1$par[6],fit1$par[7],fit1$par[8],"fmkl",fit1$par[9])
#Compare this with the empirical moments from the data set.
fun.moments.r(faithful[,1])
#Do a quantile plot
qqplot.gld.bi(faithful[,1],fit1$par,param1="fmkl",param2="fmkl",
name="FMKL FMKL ML fit")
#Quantile matching method
#Fitting faithful data from the dataset library, with the clara clustering
#regime. The first distribution is RS and the second distribution is fmkl.
#The percentage of data mix is 1%.
#Fitting normal(3,2) distriution using the default setting
junk<-rnorm(50,3,2)
fun.data.fit.qs(junk)
fun.auto.bimodal.qs(faithful[,1],per.of.mix=0.01,clustering.m=clara,
init1.sel="rprs",init2.sel="rmfmkl",init1=c(-1.5,1,5),init2=c(-0.25,1.5),
leap1=3,leap2=3)
#L Moment matching
#Fitting normal(3,2) distriution using the default setting
junk<-rnorm(50,3,2)
fun.data.fit.lm(junk)
# Moment matching method
#Fitting normal(3,2) distriution using the default setting
junk<-rnorm(50,3,2)
fun.data.fit.mm(junk)
# Example on fitting mixture of normal distributions
data1<-c(rnorm(1500,-1,2/3),rnorm(1500,1,2/3))
junk<-fun.auto.bimodal.ml(data1,per.of.mix=0.01,clustering.m=data1>0,
init1.sel="rprs",init2.sel="rmfmkl",init1=c(-1.5,1.5),init2=c(-0.25,1.5),
leap1=3,leap2=3)
fun.plot.fit.bm(nclass=50,fit.obj=junk,data=data1,
name="Maximum likelihood using",xlab="faithful1",param.vec=c("rs","fmkl"))
qqplot.gld.bi(data1,junk$par,param1="rs",param2="fmkl",
name="RS FMKL ML fit",range=c(0.001,0.999))
# Generate random observations from FMKL generalised lambda distributions with
# parameters (1,2,3,4) and (4,3,2,1) with 50% of data from each distribution.
fun.simu.bimodal(c(1,2,3,4),c(4,3,2,1),prop1=0.5,param1="fmkl",param2="fmkl")
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