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• Open Access   Article

  Univariate frailty distributions: A Review

  S.G.Parekh, S.R. Patel

  Review Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.352-356, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.352356

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  Abstract
  The main idea of this review article is to review different univariate frailty models discussed by various authors. Particularly Discrete, Gamma, Inverse Gaussian, Generalized exponential, Log normal, Compound Poisson and Compound Negative Binomial frailty distributions are discussed. So far we have furnished the development of different frailty distributions with some important features and we have also provided the recent developments of many frailty distributions. By generating the observations of some distributions, we have obtained maximum likelihood estimators of the parameters with their standard errors involved in these frailty distributions.

  Key-Words / Index Term
  Frailty models, Gamma, Inverse Gaussian, Generalized exponential, Log normal, Compound Poisson, Compound Negative Binomial, distributions

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  Citation
  S.G.Parekh, S.R. Patel, "Univariate frailty distributions: A Review," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.352-356, 2018

• Open Access   Article

  Further Results on Accurate Domination in Graphs

  B. Basavanagoud, Sujata Timmanaikar

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.357-361, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.357361

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  Abstract
  The accurate domination number of graph denoted by is the cardinality of a smallest set that is dominating set of and no element subset of is a dominating set of In this paper, we characterized the graphs with equal accurate domination number and maximal domination number( ). Further, we obtained various bounds for in terms of minimum(maximum)degree, vertex(edge)connectivity, vertex(edge)covering number, chromatic number and domination(connected domination)number.

  Key-Words / Index Term
  Domination number, Accurate domination number, Maximal domination number

  References
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  Citation
  B. Basavanagoud, Sujata Timmanaikar, "Further Results on Accurate Domination in Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.357-361, 2018

• Open Access   Article

  Bayesian Estimation via numerical approximations under Progressive Type II Censoring

  Ranjita Pandey, Neera Kumari

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.362-379, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.362379

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  Abstract
  Classical and Bayesian estimation of the unknown parametric functions for power generalized Weibull distribution under progressive Type II censoring scheme are undertaken in the present paper. Newton Raphson iterative procedure is used for computation of maximum likelihood estimates which are not obtained in closed form. Asymptotic and bootstrap confidence intervals are also obtained. Squared error and general entropy loss functions are considered for Bayes estimation under the assumption of two independent gamma priors. The approximate Bayes estimates are obtained using Tierney-Kadane approximation. Alternatively, Meteropolis Hastings algorithm is run under Gibbs sampler environment to generate Bayes etimates. Computed Bayes estimates are compared with the classical maximum likelihood estimates based a simulated data and a real data set.

  Key-Words / Index Term
  Type II progressive right censoring scheme, Boot-p and Boot-t intervals, Tierney and Kadane method, Markov Chain Monte Carlo.

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  Citation
  Ranjita Pandey, Neera Kumari, "Bayesian Estimation via numerical approximations under Progressive Type II Censoring," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.362-379, 2018