A Class of Multivariate Power Skew Symmetric Distributions: Properties and Inference for the Power-Parameter

Arnold, S. F. (1985). Sufficiency and invariance. Stat. Probab. Lett.3, 275–279.

Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Stat., 171–178.

Barndorff-Nielsen (2014). Information and exponential families: in statistical theory. Wiley.

Basawa, I. V. (1981). Efficient conditional tests for mixture experiments with applications to the birth and branching processes. Biometrika 68, 153–164.

Basu, D. (1959). The family of ancillary statistics. Sankhyā: Indian J. Stat., 247–256.

Basu, D. (1964). Recovery of ancillary information. Sankhyā: Indian J. Stat. 26, 3–16.

Basu, D. (1977). On the elimination of nuisance parameters. J. Am. Stat. Assoc. 72, 365–366.

Berk, R. H. (1972). A note on sufficiency and invariance. Ann. Math. Stat. 43, 647–650.

Cox, D. R. (1975). Partial likelihood. Biometrika 62, 269–276.

Durrans, S. R. (1992). Distributions of fractional order statistics in hydrology. Water Resour. Res. 28, 1649–1655.

Fernandez, C., Osiewalski, J. and Steel, M. F. J. (1995). Modeling and inference with υ-spherical distributions. J. Am. Stat. Assoc. 90, 1331–1340.

Gomez, H. W., Salinas, H. S. and Bolfarine, H. (2006). Generalized skew-normal models: properties and inference. Statistics 40, 495–505.

Gupta, R. D. and Gupta, R. C. (2008). Analyzing skewed data by power normal model. Test 17, 197–210.

Gupta, A. K., Chang, F. C. and Huang, W. J. (2002). Some skew-symmetric models. Random Oper. Stoch. Equ. 10, 133–140.

Hall, W. J., Wijsman, R. A. and Ghosh, J. K. (1965). The relationship between sufficiency and invariance with applications in sequential analysis. Ann. Math. Stat. 36, 575–614.

Johnson, R. A. and Wichern, D. W. (2014). Applied multivariate statistical analysis, vol 6. Pearson, London.

Justel, A., Peña, D. and Zamar, R. (1997). A multivariate kolmogorov-smirnov test of goodness of fit. Stat. Probab. Lett. 35, 251–259.

Kariya, T. (1989). Equivariant estimation in a model with an ancillary statistic. Ann. Stat., 920–928.

Koehler, E., Brown, E. and Haneuse, S. J. -P. (2009). On the assessment of monte carlo error in simulation-based statistical analyses. Am. Stat. 63, 155–162.

Landers, D. and Rogge, L. (1973). On sufficiency and invariance. Ann. Stat. 1, 543–544.

Lehmann, E.L. and Casella, G. (2006). Theory of point estimation. Springer Science & Business Media.

Mudholkar, G. S. and Hutson, A. D. (2000). The epsilon–skew–normal distribution for analyzing near-normal data. J. Stat. Plan. Inference 83, 291–309.

Pewsey, A., Gomez, H. W. and Bolfarine, H. (2012). Likelihood-based inference for power distributions. Test 21, 775–789.

Ramamoorthi, R. V. (1990). Sufficiency, ancillarity and independence in invariant models. J. Stat. Plan. Inference 26, 59–63.

Rattihalli, R. N. and Patil, P. Y. (2010). Generalized υ-spherical densities. Commun. Stat.—Theory Methods 39, 3568–3583.

Rattihalli, R. N. and Raghunath, M. (2019). Power skew symmetric distributions: tests for symmetry. In Proceedings of the Twelfth International Conference Minsk, September 18–22, 2019, pp. 104–113.

White, I. R. (2010). simsum: analyses of simulation studies including Monte Carlo error. Stata J. 10, 369–385.