References
- Arnold , B. C. , Beaver , R. J. ( 2000 ). Hidden truncation models . Sankhya Ser A 62 : 22 – 35 .
- Arnold , B. C. , Beaver , R. J. ( 2002 ). Skewed multivariate models related to hidden truncation and/or selective sampling . Test 11 : 7 – 54 .
- Azzalini , A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12:171–178.
- Azzalini , A. , Dalla Valle , A. ( 1996 ). The multivariate skew-normal distribution . Biometrika 83 : 715 – 726 .
- Azzalini , A. , Capitanio , A. ( 2003 ). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-t distribution . J. Roy. Statist. Soc. B 65 : 367 – 389 .
- Baggs , G. E. , Nagaraja , H. N. ( 1996 ). Reliability properties of order statistics from bivariate exponential distributions . Commun. Statist. Stochastic Models 12 : 611 – 631 .
- Barlow , R. E. , Proschan , F. ( 1975 ). Statistical Theory of Reliability and Life Testing . New York : Holt, Rinehart and Winston .
- Block , H. W. , Li , Y. , Savits , T. H. ( 2003 ). Initial and final behaviour of failure rate functions for mixtures and systems . J. Appl. Probab. 40 : 721 – 740 .
- Burridge , J. ( 1981 ). A note on maximum likelihood estimation for regression problems using grouped data . J. Roy. Statist. Soc. B 43 : 41 – 45 .
- Cain , M. ( 1994 ). The moment-generating function of the minimum of bivariate normal random variables . Amer. Statist. 48 : 124 – 125 .
- Cain , M. , Pan , M. ( 1995 ). Moments of the minimum of bivariate normal random variables . Math. Sci. 20 : 119 – 122 .
- Chiogna , M. ( 2005 ). A note on the asymptotic distribution of the maximum likelihood estimator for the scalar skew-normal distribution . Statist. Methods Appl. 14 : 331 – 341 .
- Cox , D. R. , Wermuth , N. ( 1991 ). A simple approximation for bivariate and trivariate normal integrals . Int. Statist. Rev. 59 : 263 – 269 .
- Dalla Valle , A. ( 2004 ). The skew-normal distribution . In: Genton , M. G. , ed. Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality . Boca Raton , FL : Chapman & Hall/CRC , pp. 3 – 24 .
- Domínguez-Molina , J. A. , González-Farías , G. , Ramos-Quiroga , R. ( 2004 ). Skew-normality in stochastic frontier analysis . In: Genton , M. G. , ed. Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality . Boca Raton , FL : Chapman & Hall/CRC , pp. 223 – 241 .
- González-Farías , G. , Domínguez-Molina , J. A. , Gupta , A. K. ( 2003 ). Additive properties of skew-normal random vectors . J. Statist. Plann. Infer. 126 ( 2 ): 521 – 534 .
- González-Farías , G. , Domínguez-Molina , J. A. , Gupta , A. K. ( 2004 ). The closed skew-normal distribution . In: Genton , M. G. , ed. Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality . Boca Raton , FL : Chapman & Hall/CRC , pp. 25 – 42 .
- Gupta , S. S. , Pillai , S. ( 1965 ). On linear functions of ordered correlated normal random variables . Biometrika 52 : 367 – 379 .
- Gupta , R. C. , Brown , N. ( 2001 ). Reliability studies of the skew-normal distribution and its application to a strength-stress model . Commun. Statist. Stochastic Models 30 ( 11 ):2427–2445.
- Gupta , P. L. , Gupta , R. C. ( 2001 ). Failure rate of the minimum and maximum of a multivariate normal distribution . Metrika 53 : 39 – 49 .
- Gupta , R. C. , Gupta , R. D. ( 2004 ). Generalized skew normal model . Test 13 : 501 – 524 .
- Kella , O. ( 1986 ). On the distribution of maximum of bivariate normal random variables with general means and variances . Commun. Statist. Theor. Meth. 15 : 3265 – 3276 .
- Liseo , B. , Loperfido , N. ( 2003 ). A Bayesian interpretation of the multivariate skew-normal distribution . Statist. Probab. Lett. 61 : 395 – 401 .
- Loperfido , N. ( 2002 ). Statistical implications of selectively reported inferential results . Statist. Probab. Lett. 56 : 13 – 22 .
- Mi , J. , Shaked , M. ( 2002 ). Stochastic dominance of random variables implies the dominance of their order statistics . J. Indian Statist. Assoc. 40 : 161 – 168 .
- Miwa , T. , Hayter , A. J. , Kuriky , S. , ( 2003 ). The evaluation of general non-centered orthant probabilities . J. Roy. Statist. Soc. B 65 : 223 – 234 .
- Nagaraja , H. N. (1982). A note on linear functions of ordered correlated normal random variables. Biometrika 69:284–285.
- Navarro , J. , Ruiz , J. M. , Sandoval , C. J. ( 2005 ). A note on comparisons among coherent systems with dependent components using signatures . Statist. Probab. Lett. 72 : 179 – 185 .
- Navarro , J. , Ruiz , J. M. , Sandoval , C. J. ( 2007 ). Properties of coherent systems with dependent components . Commun. Statist. Theor. Meth. 36 : 175 – 191 .
- Olkin , I. , Viana , M. ( 1995 ). Correlation analysis of extreme observations from a multivariate normal distribution . J. Amer. Statist. Assoc. 90 : 1373 – 1379 .
- Page , E. ( 1977 ). Approximations to the cumulative normal function and its inverse for use on a pocket calculator . Appl. Statist. 26 : 75 – 76 .
- Peristiani , S. ( 1991 ). The ℱ-system distribution as an alternative to multivariate normality: an application in multivariate models with qualitative dependent variables . Commun. Statist. Theor. Meth. 20 : 147 – 163 .
- Pewsey , A. ( 2000 ) Problems of inference for Azzalini's skew-normal distribution . J. Appl. Statist. 27 : 859 – 870 .
- Roberts , C. ( 1966 ). A correlation model useful in the study of twins . J. Amer. Statist. Assoc. 61 : 1184 – 1190 .
- Ruiz , J. M. , Navarro , J. ( 1994 ). Characterization of distributions by relationships between failure rate and mean residual life . IEEE Trans. Reliab. 43 : 640 – 644 .
- Shaked , M. , Shanthikumar , J. G. ( 1994 ). Stochastic Orders and Their Applications . San Diego : Academic Press .
- Viana , M. ( 1998 ). Linear combinations of ordered symmetric observations with application to visual acuity . In: Balakrishnan , N. , Rao , C. R. , eds. Handbook of Statistics 17. Order Statistics: Applications . Amsterdam : North-Holland , pp. 513 – 524 .
- Waldman , D. M. ( 1982 ). A stationary point for the stochastic frontier likelihood . J. Econometrics 18 : 275 – 279 .