# finder.r                  
 #  Example 8.3 -- maximize likelihood/root of likelihood equation
 #
 #  data
  x <- c(1,1,1,1,1,1,2,2,2,3)
 #                  define log-likelihood function
    llike <- function (theta) { # loglikelihood for log-series model
             n <- length(x) 
             sumx <- sum(x)
             llike <-  sumx*log(theta) - n*log(-log(1-theta)) }
 #                  derivative log-likelihood function
    dllike <- function (theta,u) { # derivative of log-series llike 
             n <- length(u) 
             sumu <- sum(u)
            dllike <- sumu/theta + n/((1-theta)*log(1-theta)) }
 #                  another way to define & use function
    dllikex <- function(theta) dllike(theta,x)
 #  
 #  maximize llike
    that1 <- optimize(f=llike, c(.02,.98), maximum=TRUE )
    print("maximize loglikelihood")
    that1
    print("value at maximum")
    t <-that1$maximum
    t
    f <- llike(t)
    f
 #  find root of likelihood equation
    that2 <- uniroot(f=dllike, lower=.02, upper=.98, u=x )
    print("root of likelihood equation")
    that2
    print("value at root")
    t <- that2$root
    t
    f <- llike(t)
    f
 #  find root of likelihood equation                v nothing passed
    that3 <- uniroot(f=dllikex, lower=.02, upper=.98 )
    print("root of likelihood equation")
    that3
    print("value at root")
    t <- that3$root
    t
    f <- llike(t)
    f
 #                  done
    rm(list=ls())
  q()