rao <- function(x,lambda) {

# *************************************************************************
#
# FILE: rao.m
#
# Date Created: Feb 4, 2004
# Author: Mark E. Irwin
#
# Contents:  Calculates the first derivative of the log likelihood for the
#            AB|ab x AB|ab linkage analysis from Rao, 1973.  Uses the
#            alternative parametrization of lambda = 1 - 2 theta + theta^2.
#            The functions allows for different data sets to be used, not
#            just the standard one used in most papers.
#
# Revision History
# Date          Name            Changes/Reasons
#
# *************************************************************************
#
# Input:
#
#   x: the vector of counts for AB, Ab, aB, and ab phenotypes
#   lambda: parameter value of interest (= 1 - 2 theta + theta^2)
#           (the actual data is [125 18 20 34])
#
# Output:
#
#   y: derivative of the log likelihood
#
# *************************************************************************


y <- x[1]/(2+lambda) - (x[2] + x[3])/(1-lambda) + x[4]/lambda

y
}