Publication Cover
Statistics
A Journal of Theoretical and Applied Statistics
Volume 57, 2023 - Issue 5
158
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Characterization-based approach for construction of goodness-of-fit test for Lévy distribution

ORCID Icon & ORCID Icon
Pages 1087-1116 | Received 18 Aug 2022, Accepted 14 Jul 2023, Published online: 24 Jul 2023

References

  • Zolotarev VM. One-dimensional stable distributions. Vol. 65. Providence (RI): American Mathematical Society; 1986.
  • Ebeling W, Romanovsky M, Sokolov I. Velocity distributions and kinetic equations for plasmas including Levy type power law tails. Contrib Plasma Phys. 2009;49(10):704–712. doi:10.1002/ctpp.v49:10
  • Rogers GL. Multiple path analysis of reflectance from turbid media. JOSA A. 2008;25(11):2879–2883. doi:10.1364/JOSAA.25.002879
  • Vinaya M, Ignatius RP. Effect of Lévy noise on the networks of Izhikevich neurons. Nonlinear Dyn. 2018;94(2):1133–1150. doi:10.1007/s11071-018-4414-8
  • West BJ, Allegrini P, Grigolini P. Dynamical generators of Lévy statistics in biology. In: Fractals in biology and medicine. Basel: Birkhäuser; 1998. p. 17–29.
  • Ali MM, Woo J. Inference on reliability P (Y< X) in the Levy distribution. Math Comput Model. 2005;41(8-9):965–971. doi:10.1016/j.mcm.2004.06.020
  • Achcar JA, Coelho-Barros EA, Cuevas JRT, et al. Use of Lévy distribution to analyze longitudinal data with asymmetric distribution and presence of left censored data. Commun Stat Appl Methods. 2018;25(1):43–60. doi:10.29220/CSAM.2018.25.1.043
  • Nolan JP. Maximum likelihood estimation and diagnostics for stable distributions; 2001.
  • Tian G. Parameter estimation for stable distribution: spacing based and indirect inference [PhD thesis]. UC Santa Barbara; 2016.
  • McCulloch JH. Simple consistent estimators of stable distribution parameters. Commun Stat-Simulation Comput. 1986;15(4):1109–1136. doi:10.1080/03610918608812563
  • Koutrouvelis IA. Regression-type estimation of the parameters of stable laws. J Am Stat Assoc. 1980;75(372):918–928. doi:10.1080/01621459.1980.10477573
  • Lilliefors HW. On the Kolmogorov-Smirnov test for normality with mean and variance unknown. J Am Stat Assoc. 1967;62(318):399–402. doi:10.1080/01621459.1967.10482916
  • O'Reilly F, Rueda R. A note on the fit for the Levy distribution. Commun Stat – Theory Methods. 1998;27(7):1811–1821. doi:10.1080/03610929808832191
  • Pitera M, Chechkin A, Wyłomańska A. Goodness-of-fit test for α-stable distribution based on the quantile conditional variance statistics. Stat Methods Appl. 2022;31(2):387–424. doi:10.1007/s10260-021-00571-9
  • Bhati D, Kattumannil SK. Jackknife empirical likelihood test for testing one-sided Lévy distribution. J Appl Stat. 2020;47(7):1208–1219. doi:10.1080/02664763.2019.1672630
  • Cuparić M, Milošević B, Obradović M. New L2-type exponentiality tests. SORT. 2019;43(1):25–50. doi:10.2436/20.8080.02.78
  • Milošević B. Asymptotic efficiency of new exponentiality tests based on a characterization. Metrika. 2016;79(2):221–236. doi:10.1007/s00184-015-0552-x
  • Milošević B, Obradović M. Some characterization based exponentiality tests and their Bahadur efficiencies. Publ Inst Math. 2016;100(114):107–117. doi:10.2298/PIM1614107M
  • Obradović M, Jovanović M, Milošević B. Goodness-of-fit tests for Pareto distribution based on a characterization and their asymptotics. Statistics. 2015;49(5):1026–1041. doi:10.1080/02331888.2014.919297
  • Allison J, Milošević B, Obradović M, et al. Distribution-free goodness-of-fit tests for the pareto distribution based on a characterization. Comput Stat. 2022;37(1):403–418. doi:10.1007/s00180-021-01126-y
  • Nikitin YY, Ragozin I. Goodness-of-fit tests for the logistic address family. J Appl Stat. 2020;47(13-15):2610–2622. doi:10.1080/02664763.2020.1761952
  • Cuparić M, Milošević B, Obradović M. New consistent exponentiality tests based on V-empirical Laplace transforms with comparison of efficiencies. Rev R Acad Cienc Exact Físic Natural Ser A Mate. 2022;116(42):1–26. doi:10.1007/s13398-021-01184-3
  • Meintanis S, Milošević B, Obradović M. Bahadur efficiency for certain goodness-of-fit tests based on the empirical characteristic function. Metrika. 2022;1–29. doi:10.1007/s13398-021-01184-3
  • Nikitin YY. Asymptotic efficiency of nonparametric tests. New York: Cambridge University Press; 1995.
  • Ebner B. The test of exponentiality based on the mean residual life function revisited. J Nonparametr Stat. 2023;1–21. doi:10.1080/10485252.2023.2178831
  • Ragozin IA. New goodness-of-fit tests for the family of Rayleigh distributions, based on a special property and a characterization. Zapiski Nauchnykh Seminarov POMI. 2021;505:230–243.
  • Ahsanullah M, Nevzorov VB. On some characterizations of the Levy distribution. Stoch Qual Control. 2019;34(1):53–57. doi:10.1515/eqc-2018-0031
  • Feller W. An introduction to probability theory and its applications. Vol. 2. New York: John Wiley & Sons; 2008.
  • Milošević B, Obradović M. New class of exponentiality tests based on U-empirical Laplace transform. Stat Pap. 2016;57(4):977–990. doi:10.1007/s00362-016-0818-z
  • Iverson H, Randles R. The effects on convergence of substituting parameter estimates into U-statistics and other families of statistics. Probab Theory Relat Fields. 1989;81(3):453–471. doi:10.1007/BF00340061
  • Nikitin YY, Peaucelle I. Efficiency and local optimality of nonparametric tests based on U-and V-statistics. Metron. 2004;62(2):185–200.
  • Raghavachari M. On a theorem of Bahadur on the rate of convergence of test statistics. Ann Math Stat. 1970;41(5):1695–1699. doi:10.1214/aoms/1177696813
  • Bahadur RR. Rates of convergence of estimates and test statistics. Ann Math Stat. 1967;38(2):303–324. doi:10.1214/aoms/1177698949
  • Ley C, Paindaveine D. Le Cam optimal tests for symmetry against Ferreira and Steel's general skewed distributions. J Nonparametr Stat. 2009;21(8):943–967. doi:10.1080/10485250902971765
  • Janssen A. Global power functions of goodness of fit tests. Ann Stat. 2000;28(1):239–253. doi:10.1214/aos/1016120371
  • Novoa-Muñoz F, Jiménez-Gamero M. Testing for the bivariate poisson distribution. Metrika. 2014;77(6):771–793. doi:10.1007/s00184-013-0464-6
  • Korolyuk VS, Borovskich YV. Theory of U-statistics. Vol. 273. Dodrecht: Springer Science & Business Media; 2013.
  • Billingsley P. Convergence of probability measures. New York: John Wiley & Sons; 1968.
  • Marcus MB, Shepp LA. Sample behavior of Gaussian processes. In: Proceedings of the sixth Berkeley symposium on mathematical statistics and probability. vol. 2; 1972. p. 423–421.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.