Anthony Pakes

Professor, MSc Melb., PhD Monash, ARMIT

  • The University of Western Australia (M019), 35 Stirling Highway,

    6009 Perth

    Australia

  • 872 Citations
  • 19 h-Index
1992 …2019
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Research Output 1992 2019

2019

Self-Decomposable Laws from Continuous Branching Processes

Pakes, A. G., 26 Feb 2019, In : Journal of Theoretical Probability.

Research output: Contribution to journalArticle

Branching process
Decomposable
Cumulants
Martingale
Tail
2018
2 Citations (Scopus)

The Lambert W function, Nuttall's integral, and the Lambert law

Pakes, A. G., 1 Aug 2018, In : Statistics and Probability Letters. 139, p. 53-60 8 p.

Research output: Contribution to journalArticle

Bernstein Function
Refinement
Evaluation
Integral

Weak and one-sided strong laws for random variables with infinite mean

Adler, A. & Pakes, A. G., 1 Nov 2018, In : Statistics and Probability Letters. 142, p. 8-16 9 p.

Research output: Contribution to journalArticle

Strong Laws
Stable Distribution
Random variable
Weak law of large numbers
Regular Variation
2017
Open Access
Markov Branching Process
Limit Theorems
Convergence Rate
Optimal Rate of Convergence
Specification
3 Citations (Scopus)

On relative stability and weighted laws of large numbers

Adler, A. & Pakes, A. G., 1 Mar 2017, In : Extremes. 20, 1, p. 1-31

Research output: Contribution to journalArticle

Relative Stability
Stable Laws
Law of large numbers
Convolution
Random variables
2015

Lambert's W meets Kermack-McKendrick Epidemics

Pakes, A., 2015, In : IMA Journal of Applied Mathematics. 80, 5, p. 1368-1386

Research output: Contribution to journalArticle

Branch Point
Elementary Functions
Transcendental
Epidemic Model
Approximation
2014

Advances in Mathematics and Statistics in Western Australia since 1960

Bassom, A., Hopwood, J., Noakes, L., Pakes, A. & Praeger, C., 2014, In : Journal of the Royal Society of Western Australia. 97, p. 253-260

Research output: Contribution to journalReview article

5 Citations (Scopus)

On generalized stable and related laws

Pakes, A., 2014, In : Journal of Mathematical Analysis and Applications. 411, 1, p. 201-222

Research output: Contribution to journalArticle

Stable Laws
Self-decomposability
Infinite Divisibility
Determinacy
Scaling

On the preservation of infinite divisibility under length-biasing

Pakes, A., 2014, In : Electronic Journal of Probability. 2014, p. 1-9

Research output: Contribution to journalArticle

Open Access
Infinite Divisibility
Infinitely Divisible
Preservation
Distribution Function
Compound Poisson
2013

A note on the gaps in the support of discreetly infinitely divisible laws

Pakes, A. & Satheesh, S., 2013, In : ISRN Probability and Statistics. 2013, p. 1-4

Research output: Contribution to journalArticle

Open Access
1 Citation (Scopus)

Limit laws for UGROW random graphs

Pakes, A., 2013, In : Statistics and Probability Letters. 83, 12, p. 2607-2614

Research output: Contribution to journalArticle

Limit Laws
Random Graphs
Gamma function
Random Forest
Limit Theorems

Limit theorems for record counts and times in the F α-scheme

Doukhan, P., Klesov, O. I., Pakes, A. & Steinebach, J. G., 2013, In : Extremes: statistical theory and applications in science, engineering and economics. 16, 2, p. 147-171

Research output: Contribution to journalArticle

Limit Theorems
Count
Record Times
Random Environment
Limiting Behavior
2012
7 Citations (Scopus)

Asymptotic Properties of the Markov Branching Process with Immigration

Li, J., Chen, A. & Pakes, A., 2012, In : Journal of Theoretical Probability. 25, p. 122-143

Research output: Contribution to journalArticle

12 Citations (Scopus)

Some properties of the exponential distribution class with applications to risk theory

Cheng, D., Ni, F., Pakes, A. & Wang, Y., 2012, In : Journal of the Korean Statistical Society. 41, 4, p. 515-527

Research output: Contribution to journalArticle

2011
12 Citations (Scopus)

Lambert's W, infinite divisibility and Poisson mixtures

Pakes, A., 2011, In : Journal of Mathematical Analysis and Applications. 378, p. 480-492

Research output: Contribution to journalArticle

Open Access
2010
49 Citations (Scopus)

Asymptotics of random contractions

Hashorva, E., Pakes, A. & Tang, Q. H., 2010, In : Insurance Mathematics & Economics. 47, p. 405-414

Research output: Contribution to journalArticle

10 Citations (Scopus)

CRITICAL MARKOV BRANCHING PROCESS LIMIT THEOREMS ALLOWING INFINITE VARIANCE

Pakes, A., 2010, In : Advances in Applied Probability. 42, p. 460-488

Research output: Contribution to journalArticle

26 Citations (Scopus)

Tail asymptotics under beta random scaling

Hashorva, E. & Pakes, A., 2010, In : Journal of Mathematical Analysis and Applications. 372, p. 496-514

Research output: Contribution to journalArticle

Open Access
2009
8 Citations (Scopus)

Numbers of observations near order statistics

Pakes, A., 2009, In : Australian and New Zealand Journal of Statistics. 51, 4, p. 375-395

Research output: Contribution to journalArticle

Limit Theorems
Order Statistics
Siméon Denis Poisson
Sample Size
Infinity
2008
2 Citations (Scopus)

Conditional Limit Theorems for Continuous Time and State Branching Process

Pakes, A., 2008, Records and Branching Processes. Ahsanullah, M. & Yanev, G. P. (eds.). New York: Nova Science Publishers, p. 63-103

Research output: Chapter in Book/Conference paperChapter

Order statistics and renormalization

Pakes, A., 2008, In : Statistics & Probability Letters. 78, 5, p. 463-470

Research output: Contribution to journalArticle

Order Statistics
Renormalization
Weak Limit
Limit Theorems
Strong Convergence
38 Citations (Scopus)
173 Downloads (Pure)

Properties of residuals for spatial point processes

Baddeley, A., Møller, J. & Pakes, A., 2008, In : Annals of the Institute of Statistical Mathematics. 60, 3, p. 627-649

Research output: Contribution to journalArticle

Open Access
File
Spatial Point Process
Random Measure
Point Process
Conditional Independence
Marginal Distribution
1 Citation (Scopus)

Tails of stopped random products: the factoid and some relatives

Pakes, A., 2008, In : Journal of Applied Probability. 45, 4, p. 1161-1180

Research output: Contribution to journalArticle

Tail
Tail Behavior
Factorial
Identically distributed
Exponent
2 Citations (Scopus)

The limit behavior of dual Markov Branching Processes

Li, Y., Pakes, A., Li, J. & Gu, A., 2008, In : Journal of Applied Probability. 45, 1, p. 176-189

Research output: Contribution to journalArticle

Markov Branching Process
Limit Behavior
Strong Ergodicity
Positive Recurrence
Transience
2007
21 Citations (Scopus)

Convolution equivalence and infinite divisibility : Corrections and corollaries

Pakes, A., 2007, In : Journal of Applied Probability. 44, 2, p. 294-304

Research output: Contribution to journalArticle

Infinite Divisibility
Convolution
Corollary
Closure
Infinitely Divisible Laws
21 Citations (Scopus)

Distributional characterizations through scaling relations

Pakes, A. & Navarro, J., 2007, In : Australian & New Zealand Journal of Statistics. 49, 2, p. 115-135

Research output: Contribution to journalArticle

Scaling Relations
Distribution Function
Scaling
Continuous Distributions
Power Function
8 Citations (Scopus)

Extinction and explosion of nonlinear Markov branching processes

Pakes, A., 2007, In : Journal of the Australian Mathematical Society. 82, 3, p. 403-428

Research output: Contribution to journalArticle

Markov Branching Process
Explosion
Extinction
Jump
Moment Sequence
15 Citations (Scopus)

Limit theorems for numbers of near-records

Pakes, A., 2007, In : Extremes. 10, 4, p. 207-224

Research output: Contribution to journalArticle

Limit Theorems
Record Times
Record Values
Limit Laws
Domain of Attraction
20 Citations (Scopus)

Structure of Stieltjes classes of moment-equivalent probability laws

Pakes, A., 2007, In : Journal of Mathematical Analysis and Applications. 326, 2, p. 1268-1290

Research output: Contribution to journalArticle

Distribution functions
Moment
Distribution Function
Modulation
Absolutely Continuous
2006
1 Citation (Scopus)

On a Conjecture of De La Grandville and Solow Converning Power Means

Keady, G. & Pakes, A., 2006, In : Journal of Inequalities in Pure and Applied Mathematics. 7, 3, p. 1-7

Research output: Contribution to journalArticle

Power Mean
Counterexample
2005
14 Citations (Scopus)

A characterization of continuous distributions via regression on pairs of record values

Bairamov, I., Ahsanullah, M. & Pakes, A., 2005, In : Australian & New Zealand Journal of Statistics. 47, 4, p. 543-547

Research output: Contribution to journalArticle

Record Values
Continuous Distributions
Regression
Exponential Type
Nonlinear Function
25 Citations (Scopus)

On the number and sum of near-record observations

Balakrishnan, N., Pakes, A. & Stepanov, A., 2005, In : Advances in Applied Probability. 37, 3, p. 765-780

Research output: Contribution to journalArticle

Random variables
Distribution functions
Record Times
Record Values
Continuous Distributions
2004
2 Citations (Scopus)
Moment Sequence
Fundamental Relation
Renewal
Recurrence
Excess
3 Citations (Scopus)

Convergence and Divergence of Random Series

Pakes, A., 2004, In : Australian & New Zealand Journal of Statistics. 46, 1, p. 29-40

Research output: Contribution to journalArticle

Dirichlet Series
Divergence
Divergent Series
Absolute convergence
Series
82 Citations (Scopus)

Convolution Equivalence and Infinite Divisibility

Pakes, A., 2004, In : Journal of Applied Probability. 41, 2, p. 407-424

Research output: Contribution to journalArticle

Infinite Divisibility
Convolution
Equivalence
Compound Poisson Distribution
Infinitely Divisible Distribution
10 Citations (Scopus)

Criteria for Convergence of the Number of Near Maxima for Long Tails

Pakes, A., 2004, In : Extremes. 7, 2, p. 123-134

Research output: Contribution to journalArticle

Tail
Complete Convergence
Almost Sure Convergence
Tend
Denote

Product Integration and Characterization of Probability Laws

Pakes, A., 2004, In : Journal of Applied Statistical Science. 13, 1, p. 11-31

Research output: Contribution to journalArticle

2003
14 Citations (Scopus)

Biological Applications of Branching Processes

Pakes, A., 2003, Handbook of Statistics. Shanbhag, D. N. & Rao, C. R. (eds.). Amsterdam, Netherlands: Elsevier, Vol. 21. p. 693-773

Research output: Chapter in Book/Conference paperChapter

15 Citations (Scopus)

Characterizations using weighted distributions

Pakes, A., Navarro, J., Ruiz, J. M. & Aguila, Y. D., 2003, In : Journal of Statistical Planning and Inference. 116, 2, p. 389-420

Research output: Contribution to journalArticle

Weighted Distributions
Biased
H-function
Partial Sums
Random variables
4 Citations (Scopus)

Extremes of geometric variables with applications to branching processes

Mitov, K. V., Pakes, A. & Yanev, G. P., 2003, In : Statistics & Probability Letters. 65, 4, p. 379-388

Research output: Contribution to journalArticle

Branching process
Limit Theorems
Extremes
Triangular Array
Extremum

Investigating the Structure of Truncated Levy-stable Laws

Pakes, A., 2003, Lecture Notes - Monograph Series. Goldstein, D. R. (ed.). 1st ed. Beachwood, Ohio: Institute of Mathematical Statistics, Vol. 40. p. 49-78 (Science and Statistics: A Festschrift for Terry Speed).

Research output: Chapter in Book/Conference paperChapter

2002

ASYMPTOTIC BEHAVIOUS OF MONOTONE WEAKLY-NONLINEAR RECURRENCES

Pakes, A., 2002, In : The Australian Mathematical Society Gazette. 29, 2, p. 91-98

Research output: Contribution to journalArticle

2 Citations (Scopus)

Random rates of growth and return: introducing the expo-normal distribution

De La Grandville, O., Pakes, A. & Tricot, C., 2002, In : Applied Stochastic Models in Business and Industry. 18, p. 23-51

Research output: Contribution to journalArticle

Normal distribution
Annual
Gaussian distribution
Probability Model
Standard deviation
2001
28 Citations (Scopus)

Criteria for the unique determination of probability distributions by moments

Pakes, A., Hung, W. L. & Wu, J. W., 2001, In : Australian and New Zealand Journal of Statistics. 43, 1, p. 101-111

Research output: Contribution to journalArticle

19 Citations (Scopus)

On the number of near-maximum insurance claims

Li, Y. & Pakes, A., 2001, In : Insurance: Mathematics and Economics. 28, p. 309-323

Research output: Contribution to journalArticle

25 Citations (Scopus)
2000
32 Citations (Scopus)

The number and sum of near-maxima for thin-tailed populations

Pakes, A., 2000, In : Advances in Applied Probability. 32, p. 1100-1116

Research output: Contribution to journalArticle

Population distribution
Oils and fats
Distribution functions
Tail
Limit Theorems
1999
4 Citations (Scopus)

Explicit distributional results in pattern formation II

Stefanov, V. & Pakes, A., 1999, In : Australian & New Zealand Journal of Statistics. 41, 1, p. 79-90

Research output: Contribution to journalArticle