Journal of Probability
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© 2014 , Hindawi Publishing Corporation . All rights reserved.

On the Expected Number of Limited Length Binary Strings Derived by Certain Urn Models
Mon, 27 Oct 2014 00:00:00 +0000
http://www.hindawi.com/journals/jprob/2014/646140/
The expected number of 01 strings of a limited length is a potentially useful index of the behavior of stochastic processes describing the occurrence of critical events (e.g., records, extremes, and exceedances). Such model sequences might be derived by a HoppePolya or a PolyaEggenberger urn model interpreting the drawings of white balls as occurrences of critical events. Numerical results, concerning average numbers of constrained length interruptions of records as well as how on the average subsequent exceedances are separated, demonstrate further certain urn models.
Frosso S. Makri and Zaharias M. Psillakis
Copyright © 2014 Frosso S. Makri and Zaharias M. Psillakis. All rights reserved.

The Generalized Inverse Generalized Weibull Distribution and Its Properties
Wed, 06 Aug 2014 11:38:51 +0000
http://www.hindawi.com/journals/jprob/2014/736101/
The Inverse Weibull distribution has been applied to a wide range of situations including applications in medicine, reliability, and ecology. It can also be used to describe the degradation phenomenon of mechanical components. We introduce Inverse Generalized Weibull and Generalized Inverse Generalized Weibull (GIGW) distributions. GIGW distribution is a generalization of several distributions in literature. The mathematical properties of this distribution have been studied and the mixture model of two Generalized Inverse Generalized Weibull distributions is investigated. Estimates of parameters using method of maximum likelihood have been computed through simulations for complete and censored data.
Kanchan Jain, Neetu Singla, and Suresh Kumar Sharma
Copyright © 2014 Kanchan Jain et al. All rights reserved.

On the Preservation of Infinite Divisibility under LengthBiasing
Mon, 21 Jul 2014 00:00:00 +0000
http://www.hindawi.com/journals/jprob/2014/703697/
The law of has distribution function and first moment . The law of the lengthbiased version of has by definition the distribution function . It is known that is infinitely divisible if and only if , where is independent of . Here we assume this relation and ask whether or is infinitely divisible. Examples show that both, neither, or exactly one of the components of the pair can be infinitely divisible. Some general algorithms facilitate exploring the general question. It is shown that lengthbiasing up to the fourth order preserves infinite divisibility when has a certain compound Poisson law or the Lambert law. It is conjectured for these examples that this extends to all orders of lengthbiasing.
Anthony G. Pakes
Copyright © 2014 Anthony G. Pakes. All rights reserved.

Hitting Times of Walks on Graphs through Voltages
Tue, 20 May 2014 12:52:57 +0000
http://www.hindawi.com/journals/jprob/2014/852481/
We derive formulas for the expected hitting times of general random walks on graphs, in terms of voltages, with very elementary electric means. Under this new light we revise bounds and hitting times for birthanddeath Markov chains and for walks on graphs with cutpoints, and give some exact computations on the necklace graph. We also prove Tetali’s formula for hitting times without making use of the reciprocity principle. In fact this principle follows as a corollary of our argument that also yields as corollaries the triangular inequality for effective resistances and the reversibility of the sum of hitting times around a tour.
José Luis Palacios, Eduardo Gómez, and Miguel Del Río
Copyright © 2014 José Luis Palacios et al. All rights reserved.

WienerItô Chaos Expansion of Hilbert Space Valued Random Variables
Mon, 07 Apr 2014 16:23:36 +0000
http://www.hindawi.com/journals/jprob/2014/786854/
The notion of fold iterated Itô integral with respect to a cylindrical Hilbert space valued Wiener process is introduced and the WienerItô chaos expansion is obtained for a square Bochner integrable Hilbert space valued random variable. The expansion can serve a basis for developing the Hilbert space valued analog of Malliavin calculus of variations which can then be applied to the study of stochastic differential equations in Hilbert spaces and their solutions.
M. A. Alshanskiy
Copyright © 2014 M. A. Alshanskiy. All rights reserved.

MarshallOlkin Discrete Uniform Distribution
Mon, 07 Apr 2014 11:17:36 +0000
http://www.hindawi.com/journals/jprob/2014/979312/
We introduce and characterize a new family of distributions, MarshallOlkin discrete uniform distribution. The natures of hazard rate, entropy, and distribution of minimum of sequence of i.i.d. random variables are derived. First order autoregressive (AR (1)) model with this distribution for marginals is considered. The maximum likelihood estimates for the parameters are found out. Also, the goodness of the distribution is tested with real data.
E. Sandhya and C. B. Prasanth
Copyright © 2014 E. Sandhya and C. B. Prasanth. All rights reserved.