Quantile-parameterized distribution: Difference between revisions

Revision as of 03:56, 28 July 2023

Revision as of 03:58, 28 July 2023

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== Applications ==

The original applications of QPDs were by decision analysts wishing to conveniently convert expert-assessed quantiles (e.g., 10th, 50th, and 90th quantiles) into smooth continuous probability distributions. QPDs have also been used to fit output data from simulations in order to represent those outputs (both CDFs and PDFs) as closed-form continuous distributions.<ref>[[doi:10.1287/deca.2016.0338|Keelin, T.W. (2016), Section 6.2.2, pp. 271–274.]]</ref> Used in this way, they are typically more stable and smoother than histograms. Similarly, since QPDs can impose fewer shape constraints than traditional distributions, they have been used to fit a wide range of empirical data in order to represent those data sets as continuous distributions (e.g., reflecting bimodality that may exist in the data in a straightforward manner<ref>[[doi:10.1287/deca.2016.0338|Keelin, T.W. (2016), Section 6.1.1, Figure 10, pp 266–267.]]</ref>). Quantile parameterization enables a closed-form QPD representation of known distributions whose CDFs otherwise have no closed-form expression. Keelin et al. (2019)<ref>{{cite book | url=https://dl.acm.org/doi/abs/10.5555/3400397.3400643 | isbn=9781728132839 | title=The metalog distributions and extremely accurate sums of lognormals in closed form | date=18 May 2020 | pages=3074–3085 | last1=Mustafee | first1=N. }}</ref> apply this to the sum of independent identically distributed lognormal distributions, where quantiles of the sum can be determined by a large number of simulations. Nine such quantiles are used to parameterize a semi-bounded metalog distribution that runs through each of these nine quantiles exactly. QPDs have also been applied to assess the risks of asteroid impact,<ref>[[doi:10.1111/risa.12453|Reinhardt, J.D., Chen, X., Liu, W., Manchev, P. and Pate-Cornell, M.E. (2016). “Asteroid risk assessment: A probabilistic approach.” Risk Analysis. 36 (2): 244–261]]</ref> cybersecurity,<ref name="Faber" /><ref>{{cite journal | url=https://www.sciencedirect.com/science/article/pii/S0167404819300604 | doi=10.1016/j.cose.2019.101659 | title=A Bayesian network approach for cybersecurity risk assessment implementing and extending the FAIR model | year=2020 | last1=Wang | first1=Jiali | last2=Neil | first2=Martin | last3=Fenton | first3=Norman | journal=Computers & Security | volume=89 | page=101659 | s2cid=209099797 }}</ref> biases in projections of oil-field production when compared to observed production after the fact,<ref>[{{Cite journal |url=https://www.onepetro.org/journal-paper/SPE-195914-PA Bratvold, R|doi=10.B.,2118/195914-PA Mohus,|title=Production E.,Forecasting: Petutschnig,Optimistic D.and Overconfident—Over and Bickel,over E.Again (|year=2020) |last1=Bratvold |first1=Reidar B. “Production|last2=Mohus forecasting:|first2=Erlend Optimistic|last3=Petutschnig and|first3=David overconfident—Over|last4=Bickel and|first4=Eric over|journal=Spe again.”Reservoir SocietyEvaluation of& PetroleumEngineering Engineers.|volume=23 doi:10.2118/195914-PA.]|issue=3 |pages=0799–0810 |s2cid=219661316 }}</ref> and future Canadian population projections based on combining the probabilistic views of multiple experts.<ref>{{Cite book |url=https://library.oapen.org/bitstream/handle/20.500.12657/42565/2020_Book_DevelopmentsInDemographicForec.pdf?sequence=1#page=51 |title=Developments in Demographic Forecasting |year=2020 |isbn=978-3-030-42471-8 |series=The Springer Series on Demographic Methods and Population Analysis |volume=49 |pages=43–62 |doi=10.1007/978-3-030-42472-5 |hdl=20.500.12657/42565 |s2cid=226615299}}</ref> See [[Metalog distribution#Applications|metalog distributions]] and Keelin (2016)<ref name="Keelin2016" /> for additional applications of the metalog distribution.