Goodness-of-Fit Test for One-Sided Lévy Distribution Based on Stein’s Characterization

Anupma Kumari1, Sudheesh K. Kattumannil2, Deepesh Bhati1
1Department of Statistics, Central University of Rajasthan, Ajmer, India
2Indian Statistical Institute, Chennai, India

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Ali MM, Woo J (2005) Inference on reliability $$P(Y<X)$$ in the Lévy distribution. Math Comput Model 41:965–971

Betsch S, Ebner B (2021) Fixed point characterizations of continuous univariate probability distributions and their application. Ann Inst OS Stat Math 73:31–59

Bhati D, Sudheesh KK (2020) Jackknife empirical likelihood test for testing one-sided Lévy distribution. J Appl Stat 47(7):1208–1219

Chang CH, Lin JJ, Pal N (2011) Testing the equality of several gamma means: a parametric bootstrap method with applications. Comput Stat 26:55–76

Datta S, Bandyopadhyay D, Satten GA (2010) Inverse probability of censoring weighted U-statistics for right censored data with an application to testing hypotheses. Scand J Stat 37:680–700

Duigon MT, Cooper BF (1999) Impact of a public water supply well on availability of groundwater to neighboring domestic wells near bel air, Maryland, Interim Technical Report, Department of Natural Resources, Maryland Geological Survey

Fama EF (1965) The behavior of stock-market prices. J Bus 38:34–105

Jurlewicz A, Weron K (1993) A relationship between asymmetric Lévy stable distribution and dialectic susceptibility. J Stat Phys 73:69–81

Keating JP, Glaser RE, Ketchum NS (1990) Testing hypotheses about the shape parameter of a gamma distribution. Technometrics 32:67–82

Klein JP, Moeschberger ML (1997) Survival analysis, techniques for censored and truncated data. Springer, New York

Koziol JA, Green SB (1976) A Cramer-von Mises statistic for randomly censored data. Biometrika 63:465–474

Lau AHL, Lau HS, Wingende JR (1990) The distribution of stock returns: new evidence against the stable model. J Bus Econ Stat 8(2):217–223

Lee ET, Wang JW (2003) Statistical methods for survival data analysis. Wiley, New Jersey

Lehmann EL (1951) Consistency and unbiasedness of certain nonparametric tests. Ann Math Stat 22:165–179

Lee AJ (1990) U-statistics: theory and practice. Marcel Dekker Inc., New York

Lévy P (1925) Calcul des probabilities. Gauthier-Villars, Paris

O’Reilly FJ, Rueda R (1998) A note on the fit for the Lévy distribution. Commun Stat Theory Methods 27:1811–1821

Samoradnitsky G (1994) Stable non-gaussian random processes stochastic models with infinite variance. Chappman and Hall, New York

Shu Y, Feng Q, Coit DW (2015) Life distribution analysis based on Lévy subordinators for degradation with random jumps. Nav Res Logist 62:483–492

Valencia-Orozco A, Tovar-Cuevas JR (2019) Parametric survival model based on the Lévy distribution. Commun Stat Appl Methods 26:445–461

van der Vaart AW (2000) Asymptotic statistics. Cambridge University Press, Cambridge