1
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Inference for three-parameter M-Wright distributions with applications

      Preprint
      ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          We propose point estimators for the three-parameter (location, scale, and the fractional parameter) variant distributions generated by a Wright function. We also provide uncertainty quantification procedures for the proposed point estimators under certain conditions. The class of densities includes the three-parameter one-sided and the three-parameter symmetric bimodal \(M\)-Wright family of distributions. The one-sided family naturally generalizes the Airy and half-normal models. The symmetric class includes the symmetric Airy and normal or Gaussian densities. The proposed interval estimator for the scale parameter outperformed the estimator derived in \cite{cah12} when the location parameter is zero. We obtain the asymptotic covariance structure for the scale and fractional parameter estimators, which allows estimation of the correlation. The coverage probabilities of the interval estimators slightly depend on the proposed location parameter estimators. For the symmetric case, the sample mean (or median) is favored than the median (or mean) when the fractional parameter is greater (or lesser) than 0.39106 in terms of their asymptotic relative efficiency. The estimation algorithms were tested using synthetic data and were compared with their bootstrap counterparts. The proposed inference procedures were demonstrated on age and height data.

          Related collections

          Most cited references6

          • Record: found
          • Abstract: not found
          • Article: not found

          Sample Quantiles in Statistical Packages

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Models of anomalous diffusion: the subdiffusive case

              Bookmark
              • Record: found
              • Abstract: found
              • Article: found
              Is Open Access

              Simulation and estimation for the fractional Yule process

              In this paper, we propose some representations of a generalized linear birth process called fractional Yule process (fYp). We also derive the probability distributions of the random birth and sojourn times. The inter-birth time distribution and the representations then yield algorithms on how to simulate sample paths of the fYp. We also attempt to estimate the model parameters in order for the fYp to be usable in practice. The estimation procedure is then tested using simulated data as well. We also illustrate some major characteristics of fYp which will be helpful for real applications.
                Bookmark

                Author and article information

                Journal
                2017-05-02
                Article
                1705.01216
                3708faeb-ad2c-449e-9bc1-c30d748c6db4

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                stat.ME

                Methodology
                Methodology

                Comments

                Comment on this article