## transform eq. 2 ##
t2 = function (lambda, y) {
  2*log(y^lambda / ((1-y)^(1-lambda)))
}

pow2.lambda = function (lambda, y) {
  n = length(y)
  y.lambda = t1(lambda, y)
  yl.bar = mean(y.lambda)
  sigmasq = mean((y.lambda - yl.bar)^2)
  -n/2 * log(sigmasq) - n/2 + (lambda-1)*sum(log(y))
}

lambda = seq(0.01, 0.99, by=0.01)
ll = sapply(lambda, pow2.lambda, y=t$pow)
BEST_LAMBDA = lambda[which(ll == max(ll))]
T2 = t2(BEST_LAMBDA, t$pow)