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الموضوع: Extensions to the Dirichlet distribution

  1. #1

    افتراضي Extensions to the Dirichlet distribution

    بسم الله الرحمن الرحيم

    تحية طيبة وبعد

    الملفات المرفقة عبارة عن البحث الذي أجريته لرسالة الدكتوراة عام 1999م

    وهي مرتبة رقميا

    الملفات المرفقة عددها 30 ملفا (ب. د. ف. , PDF )

    بعضها مفقود و سيتم إلحاقها مستقبلا إن شاء الله, والمفقود لا يؤثر على مجمل البحث و فكرته.

    عنوان البحث
    Extensions to the Dirichlet distribution

    for data on the simplex

    and

    extensions to the Liouville distribution

    for data on the positive orthant


    عناوين الأبواب المكونة للبحث

    Chapter 1
    Introduction, background, and overview

    Chapter 2
    Compositional data

    Chapter 3
    Known generalizations of the Dirichlet distribution

    Chapter 4
    Liouville distributions and some known generalizations

    Chapter 5
    Adaptive Dirichlet distributions with dependent ratios

    Chapter 6
    Extended Liouville distributions

    Chapter 7
    Perfect aggregation in reliability analysis

    Chapter 8
    Snowmelt runoff problem

    Chapter 9
    Simulation results

    Chapter 10
    Conclusion and suggestions for future research




    Abstract


    The primary contributions of this dissertation are:
    1)
    the development of new distributions on the unit simplex and the positive orthant;
    2)
    the application of some of our new distributions to both actual snowmelt runoff data and hypothetical simulated data,
    to compare the performance of these new distributions to that of other distributions that have been used in the past;

    and
    3)
    an application of some of these new distributions to the study of perfect aggregation in reliability analysis.

    We begin by reviewing what is known about distributions for analyzing compositional data; i.e., non-negative multivariate data that satisfy a unit-sum constraint.
    Unfortunately, the unit-sum constraint is sometimes just ignored in practice. In other cases, the Dirichlet distribution is used to model compositional data,
    even when the conditional independence properties of the Dirichlet are not appropriate to the data-generating process.
    Distributions other than the Dirichlet also have limitations, including either unknown or restrictive correlation sign structures.
    Similar problems arise for non-normal multivariate data on the positive orthant.

    Due to the above concerns, we propose new families of distributions on both the unit simplex and the positive orthant. In particular,
    we develop a generalization to the Dirichlet distribution on the unit simplex, and a generalization to the Liouville distribution on the positive orthant.
    Researchers working in this area have pointed out the importance of knowing the correlation sign structures achievable by a given model,
    but this information is not available for many existing distributions. We are able to provide closed-form expressions for the moments
    and correlation coefficients of most of the distributions developed in this dissertation, and also show that they have more flexible correlation sign structures
    than many existing distributions on the unit simplex or the positive orthant.

    Next, we apply one of our new unit simplex distributions to both actual snowmelt runoff data and hypothetical simulated data.
    Our analysis shows that this distribution is in some respects an improvement over the distribution that had been used to analyze such data in the past by other researchers.
    In particular, the distribution we developed is able to more closely match the observed (empirical or simulated) correlation matrices.

    We also explore the issue of perfect aggregation in reliability analysis (i.e., the conditions under which a Bayesian reliability analysis using only system-level data
    will yield the same results as an analysis performed using component-level data). Previous work for Bernoulli systems with dependent components was able to
    demonstrate only that perfect aggregation holds if the system state probabilities have a joint Dirichlet distribution (i.e., sufficient condition for perfect aggregation).
    We give necessary and sufficient conditions that the joint prior distribution of the system state probabilities must satisfy in order for perfect aggregation to hold for such systems,
    and also for parallel Poisson systems. We then provide a number of examples of joint probability distributions for the system state probabilities that satisfy perfect aggregation,
    including both existing probability distributions from the literature, and also some new distributions original to this dissertation.


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  2. #2

    افتراضي

    نواصل الإرفاق

    و سأتطرق مستقبلا بإذن الله إلى إمكانية الإستفادة منه في مجالات متعددة ومنها حقول
    العلوم الإنسانية والاجتماعية التي طالما اشغلني أمرها

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  3. #3

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  4. #4

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  5. #5

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  6. #6

    افتراضي

    نواصل العمل
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  7. #7

    افتراضي



    المهتم بهذا الحقل العلمي , يمكنه التواصل معي على العناوين التالية

    ys4911@gawab.com

    yousef3920***********

    من اجل السعى سويا لتوظيف هذا العلم لصالح مجتمعاتنا و قضايانا المعاصرة.


    و لمزيد من المعلومات عن هذا الحقل يمكن لكل محب مراجعة

    الرابط النتي للجماعة المهتمة بقضية نمذجة بيانات الوحدة

    http://ima.udg.edu/Activitats/CoDaWork03/

    Compositional Data Analysis Workshop
    15-17 October 2003


    =-=-=-=-=-=-=-=-=-

    http://ima.udg.edu/Activitats/CoDaWork05/

    2nd Compositional Data Analysis Workshop

    CoDaWork'05
    Girona 19-21 October 2005





  8. #8

    افتراضي

    بارك الله فيك وجزاك الله خيرا

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