Showing papers by "Palaniappan Vellaisamy published in 2017"
TL;DR: In this article, a generalization of the space-time fractional Poisson process involving the Caputo type Saigo differential operator is introduced and its state probabilities are obtained using ADM.
22 citations
TL;DR: In this article, a new method based on probability generating functions is used to obtain multiple Stein operators for various random variables closely related to Poisson, binomial and negative binomial distributions.
Abstract: In this paper, a new method based on probability generating functions is used to obtain multiple Stein operators for various random variables closely related to Poisson, binomial and negative binomial distributions. Also, the Stein operators for certain compound distributions, where the random summand satisfies Panjer’s recurrence relation, are derived. A well-known perturbation approach for Stein’s method is used to obtain total variation bounds for the distributions mentioned above. The importance of such approximations is illustrated, for example, by the binomial convoluted with Poisson approximation to sums of independent and dependent indicator random variables.
19 citations
TL;DR: In this article, the n -th Adomian polynomial for any nonlinear operator can be expressed explicitly in terms of the partial exponential Bell polynomials and some new identities are obtained by solving certain ordinary differential equations using the adomian decomposition method.
8 citations
TL;DR: In this paper, the explicit expressions for the state probabilities of various state dependent fractional point processes were obtained by employing the Adomian decomposition method to solve the difference differential equations governing state probabilities.
Abstract: We obtain the explicit expressions for the state probabilities of various state dependent fractional point processes recently introduced and studied by Garra et al. (2015). The inversion of the Laplace transforms of the state probabilities of such processes is rather cumbersome and involved. We employ the Adomian decomposition method to solve the difference differential equations governing the state probabilities of these state dependent processes. The distributions of some convolutions of the Mittag-Leffler random variables are derived as special cases of the obtained results.
4 citations
TL;DR: The concept of average collapsibility is more general than collapsibility, and requires that the conditional average of an association measure equals the corresponding marginal measure as discussed by the authors, which is a generalization of the concept of norm collapse.
Abstract: Collapsibility deals with the conditions under which a conditional (on a covariate W) measure of association between two random variables Y and X equals the marginal measure of association. In this paper, we discuss the average collapsibility of certain well-known measures of association, and also with respect to a new measure of association. The concept of average collapsibility is more general than collapsibility, and requires that the conditional average of an association measure equals the corresponding marginal measure. Sufficient conditions for the average collapsibility of the association measures are obtained. Some interesting counterexamples are constructed and applications to linear, Poisson, logistic and negative binomial regression models are discussed. An extension to the case of multivariate covariate W is also analyzed. Finally, we discuss the collapsibility conditions of some dependence measures for survival models and illustrate them for the case of linear transformation models.
1 citations
TL;DR: In this paper, the authors established the asymptotic normality of the median of the absolute residuals and median of absolute differences of pairwise residuals in the first order explosive autoregressive time series.