IDEAS home Printed from https://ideas.repec.org/a/wly/riskan/v24y2004i3p553-571.html
   My bibliography  Save this article

Quantification of Variability and Uncertainty Using Mixture Distributions: Evaluation of Sample Size, Mixing Weights, and Separation Between Components

Author

Listed:
  • Junyu Zheng
  • H. Christopher Frey

Abstract

Variability is the heterogeneity of values within a population. Uncertainty refers to lack of knowledge regarding the true value of a quantity. Mixture distributions have the potential to improve the goodness of fit to data sets not adequately described by a single parametric distribution. Uncertainty due to random sampling error in statistics of interests can be estimated based upon bootstrap simulation. In order to evaluate the robustness of using mixture distribution as a basis for estimating both variability and uncertainty, 108 synthetic data sets generated from selected population mixture log‐normal distributions were investigated, and properties of variability and uncertainty estimates were evaluated with respect to variation in sample size, mixing weight, and separation between components of mixtures. Furthermore, mixture distributions were compared with single‐component distributions. Findings include: (1) mixing weight influences the stability of variability and uncertainty estimates; (2) bootstrap simulation results tend to be more stable for larger sample sizes; (3) when two components are well separated, the stability of bootstrap simulation is improved; however, a larger degree of uncertainty arises regarding the percentiles coinciding with the separated region; (4) when two components are not well separated, a single distribution may often be a better choice because it has fewer parameters and better numerical stability; and (5) dependencies exist in sampling distributions of parameters of mixtures and are influenced by the amount of separation between the components. An emission factor case study based upon NOx emissions from coal‐fired tangential boilers is used to illustrate the application of the approach.

Suggested Citation

  • Junyu Zheng & H. Christopher Frey, 2004. "Quantification of Variability and Uncertainty Using Mixture Distributions: Evaluation of Sample Size, Mixing Weights, and Separation Between Components," Risk Analysis, John Wiley & Sons, vol. 24(3), pages 553-571, June.
    • Handle: RePEc:wly:riskan:v:24:y:2004:i:3:p:553-571
    DOI: 10.1111/j.0272-4332.2004.00459.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.0272-4332.2004.00459.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.0272-4332.2004.00459.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Yacov Y. Haimes & Timothy Barry & James H. Lambert, 1994. "When and How Can You Specify a Probability Distribution When You Don't Know Much?," Risk Analysis, John Wiley & Sons, vol. 14(5), pages 661-706, October.
    2. F. Owen Hoffman & Jana S. Hammonds, 1994. "Propagation of Uncertainty in Risk Assessments: The Need to Distinguish Between Uncertainty Due to Lack of Knowledge and Uncertainty Due to Variability," Risk Analysis, John Wiley & Sons, vol. 14(5), pages 707-712, October.
    3. Stanley Kaplan & B. John Garrick, 1981. "On The Quantitative Definition of Risk," Risk Analysis, John Wiley & Sons, vol. 1(1), pages 11-27, March.
    4. DeSarbo, W.S. & Wedel, M., 1993. "A Review of Recent Developments in Latent Class Regression Models," Papers 521, Groningen State, Institute of Economic Research-.
    5. Kenneth T. Bogen & Robert C. Spear, 1987. "Integrating Uncertainty and Interindividual Variability in Environmental Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 7(4), pages 427-436, December.
    6. Wedel, M, et al, 1993. "A Latent Class Poisson Regression Model for Heterogeneous Count Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 397-411, Oct.-Dec..
    7. David E. Burmaster & Andrew M. Wilson, 2000. "Fitting Second‐Order Finite Mixture Models to Data with Many Censored Values Using Maximum Likelihood Estimation," Risk Analysis, John Wiley & Sons, vol. 20(2), pages 261-272, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Junyu Zheng & H. Christopher Frey, 2005. "Quantitative Analysis of Variability and Uncertainty with Known Measurement Error: Methodology and Case Study," Risk Analysis, John Wiley & Sons, vol. 25(3), pages 663-675, June.
    2. John P. Saldanha & Bradley S. Price & Douglas J. Thomas, 2023. "A nonparametric approach for setting safety stock levels," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1150-1168, April.
    3. Daniel A. Griffith & Richard E. Plant, 2022. "Statistical Analysis in the Presence of Spatial Autocorrelation: Selected Sampling Strategy Effects," Stats, MDPI, vol. 5(4), pages 1-20, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. J. C. Helton & F. J. Davis, 2002. "Illustration of Sampling‐Based Methods for Uncertainty and Sensitivity Analysis," Risk Analysis, John Wiley & Sons, vol. 22(3), pages 591-622, June.
    2. Junyu Zheng & H. Christopher Frey, 2005. "Quantitative Analysis of Variability and Uncertainty with Known Measurement Error: Methodology and Case Study," Risk Analysis, John Wiley & Sons, vol. 25(3), pages 663-675, June.
    3. Bas Groot Koerkamp & Theo Stijnen & Milton C. Weinstein & M. G. Myriam Hunink, 2011. "The Combined Analysis of Uncertainty and Patient Heterogeneity in Medical Decision Models," Medical Decision Making, , vol. 31(4), pages 650-661, July.
    4. Vinish Shrestha, 2015. "Estimating the Price Elasticity of Demand for Different Levels of Alcohol Consumption among Young Adults," American Journal of Health Economics, MIT Press, vol. 1(2), pages 224-254, Spring.
    5. Decker, Reinhold & Trusov, Michael, 2010. "Estimating aggregate consumer preferences from online product reviews," International Journal of Research in Marketing, Elsevier, vol. 27(4), pages 293-307.
    6. Thomas Ying‐Jeh Chen & Valerie Nicole Washington & Terje Aven & Seth David Guikema, 2020. "Review and Evaluation of the J100‐10 Risk and Resilience Management Standard for Water and Wastewater Systems," Risk Analysis, John Wiley & Sons, vol. 40(3), pages 608-623, March.
    7. Marco Gemma & Fulvia Pennoni & Roberta Tritto & Massimo Agostoni, 2021. "Risk of adverse events in gastrointestinal endoscopy: Zero-inflated Poisson regression mixture model for count data and multinomial logit model for the type of event," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-16, June.
    8. Emanuele Borgonovo, 2008. "Epistemic Uncertainty in the Ranking and Categorization of Probabilistic Safety Assessment Model Elements: Issues and Findings," Risk Analysis, John Wiley & Sons, vol. 28(4), pages 983-1001, August.
    9. Padma Sharma, 2022. "Assessing Regulatory Responses to Banking Crises," Research Working Paper RWP 22-04, Federal Reserve Bank of Kansas City.
    10. Amirhossein Mokhtari & H. Christopher Frey, 2005. "Sensitivity Analysis of a Two‐Dimensional Probabilistic Risk Assessment Model Using Analysis of Variance," Risk Analysis, John Wiley & Sons, vol. 25(6), pages 1511-1529, December.
    11. Paul S. Price & Cynthia L. Curry & Philip E. Goodrum & Michael N. Gray & Jane I. McCrodden & Natalie W. Harrington & Heather Carlson‐Lynch & Russell E. Keenan, 1996. "Monte Carlo Modeling of Time‐Dependent Exposures Using a Microexposure Event Approach," Risk Analysis, John Wiley & Sons, vol. 16(3), pages 339-348, June.
    12. Paul S. Price & Steave H. Su & Jeff R. Harrington & Russell E. Keenan, 1996. "Uncertainty and Variation in Indirect Exposure Assessments: An Analysis of Exposure to Tetrachlorodibenzo‐p‐Dioxin from a Beef Consumption Pathway," Risk Analysis, John Wiley & Sons, vol. 16(2), pages 263-277, April.
    13. Kimberly M. Thompson, 2002. "Variability and Uncertainty Meet Risk Management and Risk Communication," Risk Analysis, John Wiley & Sons, vol. 22(3), pages 647-654, June.
    14. H. Christopher Frey & David E. Burmaster, 1999. "Methods for Characterizing Variability and Uncertainty: Comparison of Bootstrap Simulation and Likelihood‐Based Approaches," Risk Analysis, John Wiley & Sons, vol. 19(1), pages 109-130, February.
    15. Gundula Glowka & Andreas Kallmünzer & Anita Zehrer, 2021. "Enterprise risk management in small and medium family enterprises: the role of family involvement and CEO tenure," International Entrepreneurship and Management Journal, Springer, vol. 17(3), pages 1213-1231, September.
    16. Benischke, Mirko H. & Guldiken, Orhun & Doh, Jonathan P. & Martin, Geoffrey & Zhang, Yanze, 2022. "Towards a behavioral theory of MNC response to political risk and uncertainty: The role of CEO wealth at risk," Journal of World Business, Elsevier, vol. 57(1).
    17. Zhou, Yuekuan & Zheng, Siqian, 2020. "Uncertainty study on thermal and energy performances of a deterministic parameters based optimal aerogel glazing system using machine-learning method," Energy, Elsevier, vol. 193(C).
    18. S. Cucurachi & E. Borgonovo & R. Heijungs, 2016. "A Protocol for the Global Sensitivity Analysis of Impact Assessment Models in Life Cycle Assessment," Risk Analysis, John Wiley & Sons, vol. 36(2), pages 357-377, February.
    19. K. Karthikeyan & S. Bharath & K. Ranjith Kumar, 2012. "An Empirical Study on Investors’ Perception towards Mutual Fund Products through Banks with Reference to Tiruchirapalli City, Tamil Nadu," Vision, , vol. 16(2), pages 101-108, June.
    20. Nicola Paltrinieri & Nicolas Dechy & Ernesto Salzano & Mike Wardman & Valerio Cozzani, 2012. "Lessons Learned from Toulouse and Buncefield Disasters: From Risk Analysis Failures to the Identification of Atypical Scenarios Through a Better Knowledge Management," Risk Analysis, John Wiley & Sons, vol. 32(8), pages 1404-1419, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:riskan:v:24:y:2004:i:3:p:553-571. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1111/(ISSN)1539-6924 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.