ISSN:
1572-9125
Keywords:
Monte Carlo
;
integration
;
random
;
approximation
;
quadrature
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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 $$\bar f_n $$ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01966094
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