An algorithm to construct Monte Carlo confidence intervals for an arbitrary function of probability distribution parameters

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.



We derive a new algorithm for calculating an exact confidence interval for a parameter of location or scale family, based on a two-sided hypothesis test on the parameter of interest, using some pivotal quantities. We use this algorithm to calculate approximate confidence intervals for the parameter or a function of the parameter of one-parameter continuous distributions. After appropriate heuristic modifications of the algorithm we use it to obtain approximate confidence intervals for a parameter or a function of parameters for multi-parameter continuous distributions. The advantage of the algorithm is that it is general and gives a fast approximation of an exact confidence interval. Some asymptotic (analytical) results are shown which validate the use of the method under certain regularity conditions. In addition, numerical results of the method compare well with those obtained by other known methods of the literature on the exponential, the normal, the gamma and the Weibull distribution.

Full text is only available to the NTUA network due to copyright restrictions

PDF Additional material:

See also:

Our works referenced by this work:

1. D. Koutsoyiannis, Statistical Hydrology, Edition 4, 312 pages, doi:10.13140/RG.2.1.5118.2325, National Technical University of Athens, Athens, 1997.
2. E. Rozos, A. Efstratiadis, I. Nalbantis, and D. Koutsoyiannis, Calibration of a semi-distributed model for conjunctive simulation of surface and groundwater flows, Hydrological Sciences Journal, 49 (5), 819–842, doi:10.1623/hysj.49.5.819.55130, 2004.
3. 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.
4. 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.

Our works that reference this work:

1. A. Efstratiadis, A. D. Koussis, D. Koutsoyiannis, and N. Mamassis, Flood design recipes vs. reality: can predictions for ungauged basins be trusted?, Natural Hazards and Earth System Sciences, 14, 1417–1428, doi:10.5194/nhess-14-1417-2014, 2014.
2. P. Dimitriadis, and D. Koutsoyiannis, Stochastic synthesis approximating any process dependence and distribution, Stochastic Environmental Research & Risk Assessment, 32 (6), 1493–1515, doi:10.1007/s00477-018-1540-2, 2018.
3. G. Papaioannou, A. Efstratiadis, L. Vasiliades, A. Loukas, S.M. Papalexiou, A. Koukouvinos, I. Tsoukalas, and P. Kossieris, An operational method for Floods Directive implementation in ungauged urban areas, Hydrology, 5 (2), 24, doi:10.3390/hydrology5020024, 2018.
4. A. Efstratiadis, P. Dimas, G. Pouliasis, I. Tsoukalas, P. Kossieris, V. Bellos, G.-K. Sakki, C. Makropoulos, and S. Michas, Revisiting flood hazard assessment practices under a hybrid stochastic simulation framework, Water, 14 (3), 457, doi:10.3390/w14030457, 2022.
5. D. Koutsoyiannis, Stochastics of Hydroclimatic Extremes - A Cool Look at Risk, Edition 3, ISBN: 978-618-85370-0-2, 391 pages, doi:10.57713/kallipos-1, Kallipos Open Academic Editions, Athens, 2023.

Works that cite this document: View on Google Scholar or ResearchGate

Other works that reference this work (this list might be obsolete):

1. Campos, J. N.B., F. A. Souza Filho and H. V.C. Lima, Risks and uncertainties in reservoir yield in highly variable intermittent rivers: Case of the Castanhão Reservoir in semi-arid Brazil, Hydrological Sciences Journal, 59 (6), 1184-1195, 2014.

Tagged under: Papers initially rejected, Software, Stochastics, Uncertainty