The literature refers to related statistics as Moran or Moran-Darling statistics. For example, Cheng & Stephens (1989) analyze the form where is defined as above. Wong & Li (2006) use the same form as well. However, Beirlant & al. (2001) uses the form with the additional factor of inside the logged summation. The extra factors will make a difference in terms of the expected mean and variance of the statistic. For consistency, this article will continue to use the Cheng & Amin/Wong & Li form. -- Editor Cheng, R.C.H; Stephens, M. A. (1989). "A goodness-of-fit test using Moran's statistic with estimated parameters". Biometrika. 76 (2): 386–392. doi:10.1093/biomet/76.2.385. Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426. Beirlant, J.; Dudewicz, E.J.; Györfi, L.; van der Meulen, E.C. (1997). "Nonparametric entropy estimation: an overview"(PDF). International Journal of Mathematical and Statistical Sciences. 6 (1): 17–40. ISSN1055-7490. Archived from the original(PDF) on May 5, 2005. Retrieved 2008-12-31. Note: linked paper is an updated 2001 version.
Wong & Li (2006) leave out the Euler–Mascheroni constant from their description. -- Editor Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426.
Wong & Li (2006) Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426.
Wong & Li (2006). Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426.
The literature refers to related statistics as Moran or Moran-Darling statistics. For example, Cheng & Stephens (1989) analyze the form where is defined as above. Wong & Li (2006) use the same form as well. However, Beirlant & al. (2001) uses the form with the additional factor of inside the logged summation. The extra factors will make a difference in terms of the expected mean and variance of the statistic. For consistency, this article will continue to use the Cheng & Amin/Wong & Li form. -- Editor Cheng, R.C.H; Stephens, M. A. (1989). "A goodness-of-fit test using Moran's statistic with estimated parameters". Biometrika. 76 (2): 386–392. doi:10.1093/biomet/76.2.385. Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426. Beirlant, J.; Dudewicz, E.J.; Györfi, L.; van der Meulen, E.C. (1997). "Nonparametric entropy estimation: an overview"(PDF). International Journal of Mathematical and Statistical Sciences. 6 (1): 17–40. ISSN1055-7490. Archived from the original(PDF) on May 5, 2005. Retrieved 2008-12-31. Note: linked paper is an updated 2001 version.
Wong & Li (2006) leave out the Euler–Mascheroni constant from their description. -- Editor Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426.
Wong & Li (2006) Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426.
Wong & Li (2006). Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426.
Cheng & Stephens (1989). Cheng, R.C.H; Stephens, M. A. (1989). "A goodness-of-fit test using Moran's statistic with estimated parameters". Biometrika. 76 (2): 386–392. doi:10.1093/biomet/76.2.385.
Cheng & Stephens (1989). Cheng, R.C.H; Stephens, M. A. (1989). "A goodness-of-fit test using Moran's statistic with estimated parameters". Biometrika. 76 (2): 386–392. doi:10.1093/biomet/76.2.385.
Ranneby (1984). Ranneby, Bo (1984). "The maximum spacing method. An estimation method related to the maximum likelihood method". Scandinavian Journal of Statistics. 11 (2): 93–112. ISSN0303-6898. JSTOR4615946.
The literature refers to related statistics as Moran or Moran-Darling statistics. For example, Cheng & Stephens (1989) analyze the form where is defined as above. Wong & Li (2006) use the same form as well. However, Beirlant & al. (2001) uses the form with the additional factor of inside the logged summation. The extra factors will make a difference in terms of the expected mean and variance of the statistic. For consistency, this article will continue to use the Cheng & Amin/Wong & Li form. -- Editor Cheng, R.C.H; Stephens, M. A. (1989). "A goodness-of-fit test using Moran's statistic with estimated parameters". Biometrika. 76 (2): 386–392. doi:10.1093/biomet/76.2.385. Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426. Beirlant, J.; Dudewicz, E.J.; Györfi, L.; van der Meulen, E.C. (1997). "Nonparametric entropy estimation: an overview"(PDF). International Journal of Mathematical and Statistical Sciences. 6 (1): 17–40. ISSN1055-7490. Archived from the original(PDF) on May 5, 2005. Retrieved 2008-12-31. Note: linked paper is an updated 2001 version.
The literature refers to related statistics as Moran or Moran-Darling statistics. For example, Cheng & Stephens (1989) analyze the form where is defined as above. Wong & Li (2006) use the same form as well. However, Beirlant & al. (2001) uses the form with the additional factor of inside the logged summation. The extra factors will make a difference in terms of the expected mean and variance of the statistic. For consistency, this article will continue to use the Cheng & Amin/Wong & Li form. -- Editor Cheng, R.C.H; Stephens, M. A. (1989). "A goodness-of-fit test using Moran's statistic with estimated parameters". Biometrika. 76 (2): 386–392. doi:10.1093/biomet/76.2.385. Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426. Beirlant, J.; Dudewicz, E.J.; Györfi, L.; van der Meulen, E.C. (1997). "Nonparametric entropy estimation: an overview"(PDF). International Journal of Mathematical and Statistical Sciences. 6 (1): 17–40. ISSN1055-7490. Archived from the original(PDF) on May 5, 2005. Retrieved 2008-12-31. Note: linked paper is an updated 2001 version.
Wong & Li (2006) leave out the Euler–Mascheroni constant from their description. -- Editor Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426.
Wong & Li (2006) Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426.
Wong & Li (2006). Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426.
The literature refers to related statistics as Moran or Moran-Darling statistics. For example, Cheng & Stephens (1989) analyze the form where is defined as above. Wong & Li (2006) use the same form as well. However, Beirlant & al. (2001) uses the form with the additional factor of inside the logged summation. The extra factors will make a difference in terms of the expected mean and variance of the statistic. For consistency, this article will continue to use the Cheng & Amin/Wong & Li form. -- Editor Cheng, R.C.H; Stephens, M. A. (1989). "A goodness-of-fit test using Moran's statistic with estimated parameters". Biometrika. 76 (2): 386–392. doi:10.1093/biomet/76.2.385. Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426. Beirlant, J.; Dudewicz, E.J.; Györfi, L.; van der Meulen, E.C. (1997). "Nonparametric entropy estimation: an overview"(PDF). International Journal of Mathematical and Statistical Sciences. 6 (1): 17–40. ISSN1055-7490. Archived from the original(PDF) on May 5, 2005. Retrieved 2008-12-31. Note: linked paper is an updated 2001 version.
The literature refers to related statistics as Moran or Moran-Darling statistics. For example, Cheng & Stephens (1989) analyze the form where is defined as above. Wong & Li (2006) use the same form as well. However, Beirlant & al. (2001) uses the form with the additional factor of inside the logged summation. The extra factors will make a difference in terms of the expected mean and variance of the statistic. For consistency, this article will continue to use the Cheng & Amin/Wong & Li form. -- Editor Cheng, R.C.H; Stephens, M. A. (1989). "A goodness-of-fit test using Moran's statistic with estimated parameters". Biometrika. 76 (2): 386–392. doi:10.1093/biomet/76.2.385. Wong, T.S.T; Li, W.K. (2006). "A note on the estimation of extreme value distributions using maximum product of spacings". Time series and related topics: in memory of Ching-Zong Wei. Institute of Mathematical Statistics Lecture Notes – Monograph Series. Beachwood, Ohio: Institute of Mathematical Statistic. pp. 272–283. arXiv:math/0702830v1. doi:10.1214/074921706000001102. ISBN978-0-940600-68-3. S2CID88516426. Beirlant, J.; Dudewicz, E.J.; Györfi, L.; van der Meulen, E.C. (1997). "Nonparametric entropy estimation: an overview"(PDF). International Journal of Mathematical and Statistical Sciences. 6 (1): 17–40. ISSN1055-7490. Archived from the original(PDF) on May 5, 2005. Retrieved 2008-12-31. Note: linked paper is an updated 2001 version.
Ranneby (1984). Ranneby, Bo (1984). "The maximum spacing method. An estimation method related to the maximum likelihood method". Scandinavian Journal of Statistics. 11 (2): 93–112. ISSN0303-6898. JSTOR4615946.