BIT Numerical Mathematics

, Volume 6, Issue 4, pp 339–346 | Cite as

Crude Monte Carlo quadrature in infinite variance case and the Central Limit Theorem

  • Aimo Törn


After a short discussion of Monte Carlo integration the crude Monte Carlo method is tested by estimating the integrals
$$\int\limits_0^1 {\left( {\frac{1}{x}} \right)^{1/v} } dxas\bar f_n = \frac{1}{n}\sum\limits_{i = 1}^n {\left( {\frac{1}{{\xi _i }}} \right)^{1/v} ,} $$
where ξ i are independent uniformly distributed random numbers in [0, 1] andν ∈ [1, 2], in which interval\(\sigma (\bar f_n )\) is infinite. By the aid of the Central Limit Theorem an approximation for the distributions of the sums\(\bar f_n \) is obtained. The results of the Monte Carlo computations are then compared with the results obtained from the distributions of\(\bar f_n \).

Key words

Monte Carlo integration random approximation quadrature 


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Copyright information

© BIT Foundations 1966

Authors and Affiliations

  • Aimo Törn
    • 1
  1. 1.Institute of MathematicsÅbo AkademiFinland

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