estimates {bvpa}

Estimation of Block-Basu Bivariate Pareto (BBBVPA) distribution

Description

Parameters estimation of BBBVPA distribution.

Usage

estimates(
  I,
  s1.int,
  s2.int,
  a0.int,
  a1.int,
  a2.int,
  tol.est = 1e-05,
  MxIter.no = 2000,
  rate = 1e-04,
  condition = "log.L"
)

Arguments

I

bivariate observations.

s1.int

initial choice of \sigma_1.

s2.int

initial choice of \sigma_2.

a0.int

initial choice of \alpha_0.

a1.int

initial choice of \alpha_1.

a2.int

initial choice of \alpha_2.

tol.est

convergence tolerance, 0.00001 (default).

MxIter.no

maximum number of iterations, 2000 (default).

rate

step size or learning rate for gradient descent, 0.0001 (default).

condition

convergence criterion, "log.L" (default) and "p.logL".

Value

object of class "bbbvpa", a list consisting of

mu1, mu2, sigma1, sigma2, alpha0, alpha1, alpha2, iter.no

estimates of parameters and number of iteration.

data

the supplied data I.

Author(s)

Biplab Paul <[e-mail]> and Arabin Kumar Dey <[e-mail]>

Examples

# Read data
data(precipitation)
data <- as.vector(precipitation[,2])
data[is.na(data)]<-0
n <- length(data)
# Construct the three-dimensional data set
data3d <- function(data){
 u <- 12
 Y <- c()
 indx <- indx1 <- indx2 <- indx3 <- 0
 r <- 5
 i <- 2
 while(i < n){
   i <- i + 1
   if(data[i] > u || sum(data[(i-1):i]) > u || sum(data[(i-2):i]) > u){
     if(data[i] > u){imax <- i}
     if(sum(data[(i-1):i]) > u){imax <- i - 3 + which(data[(i-1):i] == max(data[(i-1):i]))[1]}
     if(sum(data[(i-2):i]) > u){imax <- i - 3 + which(data[(i-2):i] == max(data[(i-2):i]))[1]}
     if(max(indx) > (imax-r)){
       cluster <- data[(max(indx)+3):(imax+r)]
     } else{
       cluster <- data[(imax-r):(imax+r)]
     }
     cluster2 <- sapply(c(1:(length(cluster)-1)), function(j) sum(cluster[j:(j+1)]))
     cluster3 <- sapply(c(1:(length(cluster)-2)), function(j) sum(cluster[j:(j+2)]))
     indx1 <- append(indx1,imax-r-1+which(cluster==max(cluster))[1])
     indx2 <- append(indx2,imax-r-1+which(cluster2==max(cluster2)))
     indx3 <- append(indx3,imax-r-1+which(cluster3==max(cluster3)))
     Y <- rbind(Y, c(max(cluster),max(cluster2),max(cluster3)))
     indx <- append(indx,imax)
     i <- i + r
   }
 }
 return(Y)
}
I <- data3d(data)[,c(1,3)]
iniz <- intliz(I)
iniz
est <- estimates(I, iniz[1], iniz[2], iniz[3], iniz[4], iniz[5])
est[-9]
param.boot(I, iniz[1], iniz[2], iniz[3], iniz[4], iniz[5])
conf.intv(est)