D. Koutsoyiannis, and S. Kozanis, A simple Monte Carlo methodology to calculate generalized approximate confidence intervals, Research report, Contractor: [Not funded], doi:10.13140/RG.2.2.33579.85286, Hydrologic Research Center, 2005.
Determination of confidence limits of distributional parameters (either marginal or dependence) and derivative quantities (e.g. distribution quantiles) is crucial for estimation of uncertainty and risk. Analytical determination is possible in few cases only. Monte Carlo simulation is a numerical method with the potential to determine confidence limits without restrictions. However, even Monte Carlo simulation is not as direct, general and easily applicable as it may seem. Existing direct solutions are exact only in limited cases whereas if applied in other cases may result in significant errors. Extending and generalizing existing solutions, a simple Monte Carlo simulation technique is studied that can determine good approximations of confidence limits in a general setting. The proposed method is partly heuristic and simultaneously so general that needs no assumptions about the statistical behavior of the statistics under study, i.e. it can perform for any distribution with any number of parameters, and for any distributional or derivative parameter. Only the theoretical probabilistic model is needed and all other calculations are done by a number of Monte Carlo simulations without additional assumptions. Some tests of the method in cases with analytically determined confidence limits indicate impressively good performance. Even though the method has been tested for independent sequences of random variables (random samples) its general formulation allows direct application in stochastic processes with any dependence structure, provided that a stochastic generator of the process of interest exists.
Full text (295 KB)
An algorithm to construct Monte Carlo confidence intervals for an arbitrary function of probability distribution parameters
Related project: Research report
Our works that reference this work:
|1.||D. Koutsoyiannis, A. Efstratiadis, and K. Georgakakos, Uncertainty assessment of future hydroclimatic predictions: A comparison of probabilistic and scenario-based approaches, Journal of Hydrometeorology, 8 (3), 261–281, doi:10.1175/JHM576.1, 2007.|
|2.||H. Tyralis, D. Koutsoyiannis, and S. Kozanis, An algorithm to construct Monte Carlo confidence intervals for an arbitrary function of probability distribution parameters, Computational Statistics, 28 (4), 1501–1527, doi:10.1007/s00180-012-0364-7, 2013.|