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##-----obtain the initial values of parameters in different distributions----
init.para<-function(x,r,p,alpha1,alpha2,n){
r=r[r>0]
p=p[(p>0)&(p<1)]
alpha1=alpha1[alpha1>0]
alpha2=alpha2[alpha2>0]
n=n[n>0]
if(length(r)>0){
r=r[1] ##only use the first value if user inputs more than one applicable values
}else{
r=max(x) ##if there is no r input, use max(x) as initial value.
}
if(length(p)>0){
p=p[1] ##only use the first value if user inputs more than one applicable values
}else{
p=sum(x>0)/length(x) ##if there is no p input, use sum(x>0)/length(x) as initial value.
}
if(length(n)>0){
n=n[1] ##only use the first value if user inputs more than one applicable values
}else{
n=max(x)+1 ##if there is no p input, use max(x)+1 as initial value.
}
temp1=mean(x)
temp2=stats::var(x)
if(length(alpha1)>0){
alpha1=alpha1[1] ##only use the first value if user inputs more than one applicable values
}else{
alpha1=abs(temp1*(temp1*(1-temp1)/temp2-1)) ##the initial value derives from the moment estimate of beta distribution mean(mean(1-mean)/var-1).
}
if(length(alpha2)>0){
alpha2=alpha2[1] ##only use the first value if user inputs more than one applicable values
}else{
alpha2=abs((1-temp1)*(temp1*(1-temp1)/temp2-1)) ##the initial value derives from the moment estimate of beta distribution (1-mean)(mean(1-mean)/var-1).
}
return(list(r=r,p=p,alpha1=alpha1,alpha2=alpha2,n=n))
}
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