R/cMAP.R

In MHussein-S/MAPfit: pdf, cdf, quantile function, rth moment, mode, generate random variates, MLE of parameters, and goodness-of-fit measurse for the MAP distribution

cMAP<-function(r,par,distr)
{
  if(!is.list(par))
    par<- as.list(par)
  if (is.null(names(par)))
    stop("'par' must be a named list")
  ddistname <- paste("d", distr, sep = "")
  qdistname <- paste("q", distr, sep = "")
  if (!exists(ddistname, mode="function"))
    stop(paste("The ", ddistname, " distribution is not defined"))
  alphapar<-match("alpha",names(par))
  betapar<-match("beta",names(par))
  if(is.na(alphapar))
    stop(" 'alpha' parameter is not defined")
  if(is.na(betapar))
    stop(" 'beta' parameter is not defined")
  args <- names(formals(ddistname))
  alpha<-par$alpha
  beta<-par$beta
  distparn<-setdiff(names(par),c("alpha","beta"))
  distpar<-par[distparn]
  m <- match(distparn,args)
  if (any(is.na(m)))
    stop("you specifies names of parameters which are not valid for ",ddistname)
  if ((alpha < 1) | (beta < 1))
  {
    stop("MAP distribution not defined for alpha and/or beta <=1")
  }
  else if (alpha*beta==1)
    stop("MAP distribution not defined for alpha*beta=1")
  
  ########################## integrand ##########################
  
  integrand <- function(y,alpha,beta,distr,distpar,r)
  {
    qdistname <- paste("q", distr, sep = "")
    L1<-do.call(qdistname, c(list(y), as.list(distpar)))
    L1<-beta^(y^2)*alpha^y*(log(alpha)+2*y*log(beta))*(L1-mMAP(1,c(alpha=alpha,beta=beta,par),distr))^r
    L1<-L1/(alpha*beta-1)
  }
  ##################################
  a<-integrate(integrand, lower = 0, upper =1,alpha=alpha,beta=beta,distr=distr ,distpar=distpar,r=r)
  return(a$value)
}