# Interval approach challenges Monte Carlo simulation

Janne Pesonen, Eero Hyvönen

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)

### Abstract

Intervals are used to represent imprecise numerical values. Modelling uncertain values with precise bounds without considering their probability distribution is infeasible in many applications. As a solution, this paper proposes the use of probability density functions instead of intervals; we consider evaluation of an arithmetical function of random variables. Since the result density cannot in general be solved algebraically, an interval method for determining its guaranteed bounds is developed. This possibility challenges traditional Monte Carlo methods in which only stochastic characterizations for the result distribution, such as confidence bounds for fractiles, can be determined.
Original language English 155-160 6 Reliable Computing 2 2 https://doi.org/10.1007/BF02425918 Published - 1996 A1 Journal article-refereed

### Fingerprint

Random variables
Probability distributions
Probability density function
Monte Carlo methods
Monte Carlo Simulation
Arithmetical Function
Confidence Bounds
Interval Methods
Interval
Monte Carlo method
Probability Distribution
Random variable
Evaluation
Modeling
Monte Carlo simulation

### Cite this

Pesonen, Janne ; Hyvönen, Eero. / Interval approach challenges Monte Carlo simulation. In: Reliable Computing. 1996 ; Vol. 2, No. 2. pp. 155-160.
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Interval approach challenges Monte Carlo simulation. / Pesonen, Janne; Hyvönen, Eero.

In: Reliable Computing, Vol. 2, No. 2, 1996, p. 155-160.

Research output: Contribution to journalArticleScientificpeer-review

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T1 - Interval approach challenges Monte Carlo simulation

AU - Pesonen, Janne

AU - Hyvönen, Eero

PY - 1996

Y1 - 1996

N2 - Intervals are used to represent imprecise numerical values. Modelling uncertain values with precise bounds without considering their probability distribution is infeasible in many applications. As a solution, this paper proposes the use of probability density functions instead of intervals; we consider evaluation of an arithmetical function of random variables. Since the result density cannot in general be solved algebraically, an interval method for determining its guaranteed bounds is developed. This possibility challenges traditional Monte Carlo methods in which only stochastic characterizations for the result distribution, such as confidence bounds for fractiles, can be determined.

AB - Intervals are used to represent imprecise numerical values. Modelling uncertain values with precise bounds without considering their probability distribution is infeasible in many applications. As a solution, this paper proposes the use of probability density functions instead of intervals; we consider evaluation of an arithmetical function of random variables. Since the result density cannot in general be solved algebraically, an interval method for determining its guaranteed bounds is developed. This possibility challenges traditional Monte Carlo methods in which only stochastic characterizations for the result distribution, such as confidence bounds for fractiles, can be determined.

U2 - 10.1007/BF02425918

DO - 10.1007/BF02425918

M3 - Article

VL - 2

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JO - Reliable Computing

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