demonstrate knowledge, understanding and ability to identify situations where
the observed variability in data differs from that expected under a hypothesized
model and be able to use various modelling approaches in tackling such
situations.
SHORT COURSE: PROBABILITY MODELS IN SAMPLING
- Erasmus Course -
Spring Semester 2014-15
Course Content
The course consists of a series of topics on the question of the existence of discrepancies between observed and anticipated variability in the data under a hypothesized model. The topics include: Distortion of observations - Distortion models, over-dispersion, under-dispersion, inflated and deflated distributions, biased distributions, weighted distributions, damaged observations, damage models, generating models, mixtures of distributions: finite mixtures, continuous mixtures, contagion. Truncated distributions, censored distributions, generalized (clustered) distributions, stuttering distributions, randomly stopped distributions, capture recapture method. Generalized distributions arising in the context of the generalized sampling schemes. Applications to problems in life sciences, accident theory, linguistics, internet access modeling.
Learning Outcomes
Upon successful completion of this course students should be able to:
demonstrate knowledge, understanding and ability to identify situations where
the observed variability in data differs from that expected under a hypothesized
model and be able to use various modelling approaches in tackling such
situations.
produce a well structured, well written expository essay about a particular
situation and the approach chosen to tackle it.
Announcements
Students interested in the course are kindly requested to get in contact with Professor Xekalaki's Office via e-mail oxek@aueb.gr. A meeting will subsequently be arranged to determine the weekly schedule of the course. The date and place of the meeting will be announced here.
Recommended Reading
Books:
Beard, Pentikainen and Pessonen (1993).
Practical Risk Theory, 2nd edition, Chapman and Hall
Douglas J.B. (1980). Analysis with Standard
Contagious Distributions. Statistical Distributions in Scientific Work
Series 4. International Cooperative Publishing House, Fairland, Maryland USA
Everitt B.S, Hand D.J. (1981). Finite
Mixtures Distributions. Chapman and Hall, London
Grandell (1997). Mixed Poisson Process,
Chapman and Hall
Hogg and Klugman (1984). Loss Distributions.
Wiley and Sons
Johnson N.L., Kotz S., Kemp A.W. (1992).
Univariate Discrete Distributions. 2nd Edition Willey-New York
Lindsay B. (1995). Mixture Models: Theory,
Geometry and Applications. Regional Conference Series in Probability and
Statistics, Vol. 5, Institute of Mathematical Statistics and American
Statistical Association
McLachlan G., Basford K. (1988). Mixture
Models: Inference and Application to Clustering. Marcel and Decker Inc.
Ord K (1972). Families of frequency
distributions. Griffins
Patil (ed) (1984). Statistical Distributions
in Ecological Work. Vol. 4, Statistical Ecology Series
An Indicative List of Research Papers:
Charalambides, Ch. & Papageorgiou H. (1981).
“Bivariate Poisson Binomial Distributions”.
Biom. J., 23(5), 437-450.
Chatfield, C. & Theobald, C.M. (1973).
“Mixtures and Random Sums”.
The Statistician, 22(4), 281-287.
Greenwood, M. & Woods, H.M. (1919).
“The incidence of industrial accidents upon individuals
with special reference to multiple accidents”.
Industrial Fatigue Research Board, Medical Research Committee, Report No. 4. Her
Majesty's Stationery Office, London.
Dimaki, C. & Xekalaki, E. (1990).
“Identifiability of Income Distributions in the Context of
Damage and Generating Models”. Commun. Stat. A-Theor.,
19(8), 2757-2766.
Famoye, F. & Singh, K.P (2006).
“Zero-Inflated Generalized Poisson Regression Model with
an Application to Domestic Violence”. J. Data
Sci., 4, 117-130.
Gupta, P.L., Gupta, R.C. & Tripathi, R.C. (2004).
“Score Test for Zero Inflated Generalized Poisson
Regression Model”. Commun. Stat. A-Theor., 33,
47-64.
Hinde, J. & Demetrio, C.G.B. (1998).
“Overdispersion: Models and Estimation”.
Comput. Stat. Data An., 27, 151-170.
Irwin, J. (1968).
“The Generalised Waring Distribution Applied to Accident
Theory”. J. Royal Stat. Soc., A 131, 205-225.
Irwin, J. (1975).
“The Generalised Waring Distribution, Part I”.
J. Royal Stat. Soc., A 138, 18-31.
Irwin, J. (1975).
“The Generalised Waring Distribution, Part II”.
J. Royal Stat. Soc., A 138, 204-227.
Irwin, J. (1975).
“The Generalised Waring Distribution, Part III”.
J. Royal Stat. Soc., A 138, 374-384.
Karlis, D. & Xekalaki, E. (2003).
“Mixtures Everywhere”.
In: Panaretos, J (ed.) Stochastic Musings: Perspectives from the Pioneers of the
Late 20th Century, 78-95. Laurence Erlbaum, USA.
Karlis, D. & Xekalaki, E. (2005).
“Mixed Poisson Distributions”.
Int. Stat. Rev., 73(1), 35-58.
Panaretos, J. (1982).
“An Extension of the Damage Model”.
Metrika, 29, 189-194.
Panaretos, J. (1983).
“A Generating Model Involving Pascal and Logarithmic
Series Distributions”. Commun. Statist. –
Theory Meth., A 12 (7), 841-848.
Panaretos, J. (1989).
“On the Evolution of Surnames”.
Int. Stat. Rev., 57(2), 161-167.
Panaretos, J. & Xekalaki, E. (1986).
“On Some Distributions Arising From Certain Generalized
Sampling Schemes”. Commun. Statist. – Theor.
Meth., 15(3), 873-891.
Panjer, H. (1981).
“Recursive Evaluation of a Family of Compound
Distributions”. ASTIN Bulletin, 12, 22-26.
Patil, G.P. & Rao, C.R. (1978).
“Weighted Distributions and Size-Biased Sampling with
Applications to Widlife Populations and Human Families”.
Biometrics, 34, 179-189.
Patil, G.P., Rao, C.R. & Ratnaparkhi, M.V. (1986).
“On Discrete Weighted Distributions and Their Use in Model
Choise for Observed Data”. Commun. Statist. –
Theory Meth., 15, 907-918.
Sichel, H.S. (1974).
“On A Distribution Representing Sentence-Length in Written
Prose”. J. Royal Stat. Soc., A 137, 25-34.
Willmot, G. (1993).
“On Recursive Evaluation of Mixed Poisson Probabilities
and Related Quantities”. Scand. Act. J., 18,
114-133.
Xekalaki, E. (1981).
“Chance Mechanisms for the Univariate Generalized Waring
Distribution and Related Characterizations”.
Stat. Distr. Scien. W., 4, 157-171.
Xekalaki, E. (1983).
“The Univariate Generalized Waring Distribution in
Relation to Accident Theory. Proneness, Spells or Contagion?”.
Biometrics, 39(3), 887-895.
Xekalaki, E. (1983).
“Infinite Divisibility, Completeness and Regression
Properties of the Univariate Generalized Waring Distribution”,
Ann. I. Stat. Math., A 35, 279-289.
Xekalaki, E. (1983).
“A Property of the Yule Distribution and its Applications”.
Commun. Stat. A-Theor., 12(10), 1181-1189.
Xekalaki, E. (1984).
“The Bivariate Generalized Waring Distribution and its
Application to Accident Theory”. J. Royal Stat.
Soc., A 147(3), 488-498.
Xekalaki, E. (1984).
“Linear Regression and the Yule Distribution”.
J. Econometrics, 24(1), 397-403.
Xekalaki, E. (1984).
“Models Leading to the Bivariate Generalized Waring
Distribution”. Utilitas Mathematica, 25,
263-290.
Xekalaki, E. (1985).
“Factorial Moment Estimation for the Bivariate Generalized
Waring Distribution”. Statistiche Hefte, 26,
115-129.
Xekalaki, E. (1986).
“The Multivariate Generalized Waring Distribution”.
Commun. Stat. A-Theor., 15(3), 1047-1064.
Xekalaki, E. (2006).
“Under- and Overdispersion”.
In: Enc. Act. Sci., 3, 1700-1705, Wiley.
Xekalaki, E. (2014).
“On The Distribution Theory of Over-Dispersion”.
J. Stat. Distr. Appl. (to appear).
Xekalaki, E. & Zografi, M. (2008).
“The Generalized Waring Process and its Application”.
Commun. Stat. A-Theor., 37(12), 1835-1854.
Xekalaki, E. & Panaretos, J. (1983).
“Identifiability of Compound Poisson Distributions”.
Scand. Act. J., 66, 39-45.
Xekalaki, E. & Panaretos, J. (1989).
“On Some Distributions Arising in Inverse Cluster
Sampling”. Commun. Statist. – Theory Meth., 18(1), 355-366.