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Showing papers by "Palaniappan Vellaisamy published in 2016"


Journal ArticleDOI
TL;DR: In this article, the short-range dependence (SRD) property of the increments of the fractional Poisson process was discussed, and it was shown that fractional negative binomial process (FNBP) has the same property.
Abstract: We discuss the short-range dependence (SRD) property of the increments of the fractional Poisson process, called the fractional Poissonian noise. We also establish that the fractional negative binomial process (FNBP) has the long-range dependence (LRD) property, while the increments of the FNBP have the SRD property. Our definitions of the SRD/LRD properties are similar to those for a stationary process and different from those recently used in Biard and Saussereau (2014).

35 citations


Posted Content
TL;DR: It is established that the fractional negative binomial process (FNBP) has the long-range dependence (LRD) property, while the increments of the FNBP have the SRD property.
Abstract: We study the long-range dependence (LRD) of the increments of the fractional Poisson process (FPP), the fractional negative binomial process (FNBP) and the increments of the FNBP. We first point out an error in the proof of Theorem 1 of Biard and Saussereau (2014) and prove that the increments of the FPP has indeed the short-range dependence (SRD) property, when the fractional index $\beta$ satisfies $0<\beta<\frac{1}{3}$. We also establish that the FNBP has the LRD property, while the increments of the FNBP possesses the SRD property.

25 citations


Journal ArticleDOI
TL;DR: This paper introduces the simulation procedures for both processes and discusses the estimation schemes for their parameters, and studies the distributional properties of both subordinators, namely, IG and IIG processes, and also that of the FBM time changed by these subordinators.
Abstract: In this paper we study the fractional Brownian motion (FBM) time changed by the inverse Gaussian (IG) process and its inverse, called the inverse to the inverse Gaussian (IIG) process. Some properties of the time-changed processes are similar to those of the classical FBM, such as long-range dependence. However, one can also observe different characteristics that are not satisfied by the FBM. We study the distributional properties of both subordinators, namely, IG and IIG processes, and also that of the FBM time changed by these subordinators. We establish also the connections between the subordinated processes considered and the continuous-time random-walk model. For the application part, we introduce the simulation procedures for both processes and discuss the estimation schemes for their parameters. The effectiveness of these methods is checked for simulated trajectories.

24 citations


Journal ArticleDOI
TL;DR: In this article, two simple parametrization methods for calculating Adomian polynomials for several nonlinear operators, which utilize the orthogonality of functions einx, where n is an integer.
Abstract: In this paper, we discuss two simple parametrization methods for calculating Adomian polynomials for several nonlinear operators, which utilize the orthogonality of functions einx, where n is an integer. Some important properties of Adomian polynomials are also discussed and illustrated with examples. These methods require minimum computation, are easy to implement, and are extended to multivariable case also. Examples of different forms of nonlinearity, which includes the one involved in the Navier Stokes equation, is considered. Explicit expression for the n-th order Adomian polynomials are obtained in most of the examples.

15 citations


Journal ArticleDOI
TL;DR: In this article, sufficient conditions for the occurrence of boundary solutions under nonignorable nonresponse models in arbitrary three-way and n-dimensional incomplete tables with one or more variables missing were provided.

5 citations


Journal ArticleDOI
TL;DR: An asymmetric extension of Farlie–Gumbel–Morgenstern copulas studied by several authors is discussed and an expression for regression function is derived and explicit expressions for various measures of association are obtained.
Abstract: In this paper, we discuss an asymmetric extension of Farlie–Gumbel–Morgenstern copulas studied by several authors and obtain the range of the parameter. We derive an expression for regression function and the properties of these copulas are studied in detail. Also, explicit expressions for various measures of association are obtained. These measures are numerically compared for some particular parametric values of the copulas.

5 citations


Journal ArticleDOI
TL;DR: In this article, a generalized class of Farlie-Gumbel-Morgenstern copulas, called the Rodriguez-Lallena and Ubeda-Flores copula family, is discussed.
Abstract: In this note, we discuss a generalization of a subclass of the Rodriguez-Lallena and Ubeda-Flores family of copulas, through order statistics. This generalized family includes an important class of the Farlie–Gumbel–Morgenstern (FGM) family of copulas, which are widely used in statistics. We derive the expressions for regression function and cumulative conditional expectation function. The explicit expressions for some measures of dependence like Spearman’s rho, Gini’s gamma coefficient, and quadrant dependence are discussed. Finally, Spearman’s rho is numerically tabulated and compared for some generalized families of FGM copulas.

4 citations


Posted Content
TL;DR: In this article, the k-th order statistic from unit exponential distribution is represented as a sum of independent exponential rvs and it is shown that the standardized exponential spacings also follow unit exponential distributions.
Abstract: We consider the k-th order statistic from unit exponential distribution and, by computing its Laplace transform, show that it can be represented as sum of independent exponential rvs. Our proof is simple and different. It readily proves that the standardized exponential spacings also follow unit exponential distribution. Another advantage of our approach is that by computing the Laplace transform of the k-th order statistic in two different ways, we derive several interesting combinatorial identities. A probabilistic interpretation of these identities and their generalizations are also given.

3 citations


Posted Content
TL;DR: In this paper, the authors obtained some recurrence relationships among the partition vectors of the partial exponential Bell polynomials and showed that the $n$-th Adomian polynomial for any nonlinear operator can be expressed explicitly in terms of the Partial Eq.
Abstract: In this paper, we obtain some recurrence relationships among the partition vectors of the partial exponential Bell polynomials. On using such results, the $n$-th Adomian polynomial for any nonlinear operator can be expressed explicitly in terms of the partial exponential Bell polynomials. Some new identities for the partial exponential Bell polynomials are obtained by solving certain ordinary differential equations using Adomian decomposition method. The corresponding results for the partial ordinary Bell polynomials are also discussed.

2 citations


Posted Content
TL;DR: In this paper, the authors studied the non-homogeneous space-time fractional Poisson process (NSTFPP), a generalization of the time fractional poisson process.
Abstract: The space-time fractional Poisson process (STFPP), defined by Orsingher and Poilto in \cite{sfpp}, is a generalization of the time fractional Poisson process (TFPP) and the space fractional Poisson process (SFPP). We study the fractional generalization of the non-homogeneous Poisson process and call it the non-homogeneous space-time fractional Poisson process (NSTFPP). We compute their {\it pmf} and generating function and investigate the associated differential equation. The limit theorems and the law of iterated logarithm for the NSTFPP process are studied. We study the distributional properties, the asymptotic expansion of the correlation function of the non-homogeneous time fractional Poisson process (NTFPP) and subsequently investigate the long-range dependence (LRD) property of a special NTFPP. We investigate the limit theorem and the LRD property for the fractional non-homogeneous Poisson process (FNPP), studied by Leonenko et. al. (2016). Finally, we present some simulated sample paths of the NSTFPP process.

1 citations


Posted Content
TL;DR: In this paper, the authors provide characterizations for the various missing mechanisms of a variable in terms of response and non-response odds for two and three dimensional incomplete tables and propose easily verifiable procedures to evaluate the missing at random (MAR), missing completely at random and not missing at Random (NMAR) assumptions of the missing data models.
Abstract: The analysis of incomplete contingency tables is a practical and an interesting problem. In this paper, we provide characterizations for the various missing mechanisms of a variable in terms of response and non-response odds for two and three dimensional incomplete tables. Log-linear parametrization and some distinctive properties of the missing data models for the above tables are discussed. All possible cases in which data on one, two or all variables may be missing are considered. We study the missingness of each variable in a model, which is more insightful for analyzing cross-classified data than the missingness of the outcome vector. For sensitivity analysis of the incomplete tables, we propose easily verifiable procedures to evaluate the missing at random (MAR), missing completely at random (MCAR) and not missing at random (NMAR) assumptions of the missing data models. These methods depend only on joint and marginal odds computed from fully and partially observed counts in the tables, respectively. Finally, some real-life datasets are analyzed to illustrate our results, which are confirmed based on simulation studies.

01 Jan 2016
TL;DR: In this article, simple parametrization methods for calculating Adomian polynomials for several nonlinear operators, which utilize the orthogonality of functions e inx, where n is an integer, are discussed and illustrated with examples.
Abstract: In this paper, we discuss two simple parametrization methods for calculating Adomian polynomials for several nonlinear operators, which utilize the orthogonality of functions e inx , where n is an integer. Some important properties of Adomian polynomials are also discussed and illustrated with examples. These methods require minimum computation, are easy to implement, and are extended to multivariable case also. Examples of different forms of nonlinearity, which includes the one involved in the Navier Stokes equation, is considered. Explicit expression for the n-th order Adomian polynomials are obtained in most of the examples.