# -*- coding: utf-8 -*-
"""Examples chapter 7.ipynb

Automatically generated by Colaboratory.

Original file is located at
    https://colab.research.google.com/drive/11FN1EtUhj5IJwTiedX97_NYqcYN_V9U2

# Example p. 239:
"""

import numpy as np
import pandas as pd

url = "/studier/emner/matnat/math/STK3505/h20/naturaldisasters.txt"
z = pd.read_csv(url, header=None, sep='\s+')

n = len(z)
A = 20
muHat = n/A
print(muHat)

def llminuspareto(beta,z):
  alphabeta = 1/np.mean(np.log(1+z/beta))
  return(-np.log(alphabeta/beta)+(1+1/alphabeta))

from scipy.optimize import minimize_scalar

res = minimize_scalar(llminuspareto, args=(z[0]), bounds=(0.001,1000))

betahat = res.x
alphahat = 1/np.mean(np.log(1+z/betahat))
print(alphahat,betahat)