newton - fisher - rapson

#### questão 6 da lousa ####
X = rep(1:6, c(1486, 694, 195, 37, 10, 1))
n = length(X)
te = 0.3
i = 1
d = 10000

while(d > 10^(-5)){
  U = sum(X)/te[i]-n-n*exp(-te[i])/(1-exp(-te[i]))
  I = sum(X)/te[i]^2-n*exp(-te[i])/(1-exp(-te[i]))^2
  J = (n/(1-exp(-te)[i]))*(1/te[i] - exp(-te[i])/(1-exp(-te[i])))

  te[i+1] = te[i] + U/J # newton = (te[i+1] = te[i] + U/I) # escor fisher = (te[i+1] = te[i] + U/J)
  d = abs(te[i+1] - te[i])
  te[i] = te[i+1]
  i = i+1
}
plot(te)
te
#### 2 questão da losa ####
lu = 100*log(mi)-50*mi-50*log(1-exp(-mi))

u = D(expression(100*log(mi)-50*mi-50*log(1-exp(-mi))), "mi" )
u = function(mi) 100 * (1/mi) - 50 - 50 *(-mi)))
 (exp(-mi)/(1 - exp
i = D(expression(100 * (1/mi) - 50 - 50 * (exp(-mi)/(1 - exp(-mi)))), "mi")
I = function(mi) -(100 * (1/mi^2) - 50 * (exp(-mi)/(1 - exp(-mi)) + exp(-mi) * exp(-mi)/(1 - exp(-mi))^2))
u = function(mi) 100 * (1/mi) - 50 - 50 * (exp(-mi)/(1 - exp(-mi)))

te = 0.3

i = 1
d = 10000

while(d > 10^(-5)){
  te[i+1] = te[i] + u(te[i])/(-1*I(te[i]))
  d = abs(te[i+1] - te[i])
  print(d)
  te[i] = te[i+1]
  i = i+1
}
te

#### quetão 5 da losa ####

l = function(alf) sum(log(1+0.3*x) -n*log(2))
u = function(alf) sum(x/(1+alf*x))
I = function(alf) sum(x^2 / (1+alf*x)^2)

j = function(alf) -n/alf^2 + n/2*alf^3 * log((1+alf)/(1-alf))

tabela = read.table('q1_3.txt', header = TRUE, sep = ' ', dec = '.')
tabela = as.vector(tabela[,1]) #transformando em vetor



n = length(tabela)
te1 = 0
i = 1
D = 10000
tal = 0
x = tabela

while( D > 10^(-5)){

  te2 = te1 + u(te1)/I(te1)
  D = abs(te2 - te1)
  te1 = te2
  tal[i] = te1
  i = i + 1
}
tal