Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2016, Cilt: 45 Sayı: 2, 521 - 540, 01.04.2016

Öz

Kaynakça

  • F.N. David. A power function for tests of randomness in a sequence of alternatives. Biometrika, 34:335–339, 1947.
  • G. Bateman. On the power function of the longest run as a test for randomness in a sequence of alternatives. Biometrika, 35:97–112, 1948.
  • D. Barton and F. David. Non-randomness in a sequence of two alternatives. Biometrika, 45:253–256, 1958.
  • P. Shaughnessy. Multiple runs distributions: recurrences and critical values. Journal of the American Statistical Association, 76(375):732–736, 1981.
  • S. Schwager. Run probabilities in sequences of Markov dependent trials. Journal of the American Statistical Association, 78:168–175, 1983.
  • M. Koutras and V. Alexandrou. Non-parametric randomness test based on success runs of fixed length. Statistic and Probability Letters, 32:393–404, 1997.
  • D. Antzoulakos, S. Bersimis, and M. Koutras. On the distribution of the total number of run lengths. Annals of the Institute of Statistical Mathematics,, 55(4):865–884, 2003.
  • M. Koutras. Waiting time distributions associated with runs of fixed length in two-state Markov chains. Annals of the Institute of Statistical Mathematics, 49:123–139, 1997. 533
  • D.L. Antzoulakos and S. Chadjiconstantinidis. Distributions of numbers of success runs of fixed length in Markov dependent trials. Annals of the Institute of Statistical Mathematics, 53(3):599–619, 2001.
  • J. Fu, W. Lou, Z. Bai, and G. Li. The exact and limiting distributions of the number of successes in success runs within a sequence of Markov-dependent two-state trial. Annals of the Institute of Statistical Mathematics, 54:719–730, 2002.
  • J. Fou, L. Want, and W. Lou. On exact and large deviation approximation for the distribution of the longest run in a sequence of two-state Markov dependent trials. Journal of Applied Probability, 40:346–360, 2003.
  • E. Vaggelatou. On the length of the longest run in a multistate Markov chain. Statistics and Probability Letters, 62:211–221, 2003.
  • L. Savelyev and V. Balakin. The joint distribution of the number of ones and the number of 1-runs in binary markov sequences. Discrete Math. Appl., 14(4):353–372, 2004.
  • S. Eryilmaz. On the distribution and expectation of success runs in nonhomogeneous Markov dependent trials. Statistical Papers, 46:117–128, 2005.
  • S. Eryilmaz. Some results associated with the longest run statistic in a sequence of Markov dependent trials. Applied Mathematics and Computation, 175:119–130, 2006.
  • S. Demir and S. Erylmaz. Run statistics in a sequence of arbitrarily dependent binary trials. Statistical Papers. Online first, 2008.
  • S. Eryilmaz. Mean success run length. Journal of the Korean Statistical Society, 38:65–71, 2009.
  • S. Eryilmaz and F. Yalcin. Distribution of run statistics in partially exchangeable processes. Metrica, 73:293–304, 2011.
  • A.W.F. Edwards. The meaning of binomial distribution. Nature, 186:1074, 1960.
  • B. Lindqvist. A note on bernoulli trials with dependence. Scand Journal Statist, 5:205–208, 1978.
  • P. Laplace. Théorie Analytique des Probabilités. Paris, Ve. Courcier, Paris, seconde edition, 1814.
  • W. Ching and M. Ng. Markov Chains: Models, Algorithms and Applications. Springer Science + Business Media, New York, 2006.
  • F. Beaujean and A. Caldwell. A test statistic for weighted runs. Journal of Statistical Planning and Inference, 141:3437–3446, 2011.

A data driven runs test to identify first order positive Markovian dependence

Yıl 2016, Cilt: 45 Sayı: 2, 521 - 540, 01.04.2016

Öz

We propose a data driven test to identify first order positive Markovian
dependence in a Bernoulli sequence, based on a combination of two runs
tests: a well known runs test for the same purpose conditional on the
numbers of ones in the sequence, and a modified runs test independent
of the number of ones. We give analytic expressions for the exact
distribution of the modified runs test statistic and for its power; also
we built an algorithm to calculate it explicitly. To compare the power of
the tests, we calculated these for some values of the proportion of ones
and the success probability. We show that there are some intervals
for the success probability in which the new runs test surpasses the
power of the conditional test, and that the data driven test improves
the power of the two runs tests, when they are considered separately.

Kaynakça

  • F.N. David. A power function for tests of randomness in a sequence of alternatives. Biometrika, 34:335–339, 1947.
  • G. Bateman. On the power function of the longest run as a test for randomness in a sequence of alternatives. Biometrika, 35:97–112, 1948.
  • D. Barton and F. David. Non-randomness in a sequence of two alternatives. Biometrika, 45:253–256, 1958.
  • P. Shaughnessy. Multiple runs distributions: recurrences and critical values. Journal of the American Statistical Association, 76(375):732–736, 1981.
  • S. Schwager. Run probabilities in sequences of Markov dependent trials. Journal of the American Statistical Association, 78:168–175, 1983.
  • M. Koutras and V. Alexandrou. Non-parametric randomness test based on success runs of fixed length. Statistic and Probability Letters, 32:393–404, 1997.
  • D. Antzoulakos, S. Bersimis, and M. Koutras. On the distribution of the total number of run lengths. Annals of the Institute of Statistical Mathematics,, 55(4):865–884, 2003.
  • M. Koutras. Waiting time distributions associated with runs of fixed length in two-state Markov chains. Annals of the Institute of Statistical Mathematics, 49:123–139, 1997. 533
  • D.L. Antzoulakos and S. Chadjiconstantinidis. Distributions of numbers of success runs of fixed length in Markov dependent trials. Annals of the Institute of Statistical Mathematics, 53(3):599–619, 2001.
  • J. Fu, W. Lou, Z. Bai, and G. Li. The exact and limiting distributions of the number of successes in success runs within a sequence of Markov-dependent two-state trial. Annals of the Institute of Statistical Mathematics, 54:719–730, 2002.
  • J. Fou, L. Want, and W. Lou. On exact and large deviation approximation for the distribution of the longest run in a sequence of two-state Markov dependent trials. Journal of Applied Probability, 40:346–360, 2003.
  • E. Vaggelatou. On the length of the longest run in a multistate Markov chain. Statistics and Probability Letters, 62:211–221, 2003.
  • L. Savelyev and V. Balakin. The joint distribution of the number of ones and the number of 1-runs in binary markov sequences. Discrete Math. Appl., 14(4):353–372, 2004.
  • S. Eryilmaz. On the distribution and expectation of success runs in nonhomogeneous Markov dependent trials. Statistical Papers, 46:117–128, 2005.
  • S. Eryilmaz. Some results associated with the longest run statistic in a sequence of Markov dependent trials. Applied Mathematics and Computation, 175:119–130, 2006.
  • S. Demir and S. Erylmaz. Run statistics in a sequence of arbitrarily dependent binary trials. Statistical Papers. Online first, 2008.
  • S. Eryilmaz. Mean success run length. Journal of the Korean Statistical Society, 38:65–71, 2009.
  • S. Eryilmaz and F. Yalcin. Distribution of run statistics in partially exchangeable processes. Metrica, 73:293–304, 2011.
  • A.W.F. Edwards. The meaning of binomial distribution. Nature, 186:1074, 1960.
  • B. Lindqvist. A note on bernoulli trials with dependence. Scand Journal Statist, 5:205–208, 1978.
  • P. Laplace. Théorie Analytique des Probabilités. Paris, Ve. Courcier, Paris, seconde edition, 1814.
  • W. Ching and M. Ng. Markov Chains: Models, Algorithms and Applications. Springer Science + Business Media, New York, 2006.
  • F. Beaujean and A. Caldwell. A test statistic for weighted runs. Journal of Statistical Planning and Inference, 141:3437–3446, 2011.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm İstatistik
Yazarlar

Jimmy A. Corzo Bu kişi benim

Myrian E. Vergara Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 45 Sayı: 2

Kaynak Göster

APA A. Corzo, J., & Vergara, M. E. (2016). A data driven runs test to identify first order positive Markovian dependence. Hacettepe Journal of Mathematics and Statistics, 45(2), 521-540.
AMA A. Corzo J, Vergara ME. A data driven runs test to identify first order positive Markovian dependence. Hacettepe Journal of Mathematics and Statistics. Nisan 2016;45(2):521-540.
Chicago A. Corzo, Jimmy, ve Myrian E. Vergara. “A Data Driven Runs Test to Identify First Order Positive Markovian Dependence”. Hacettepe Journal of Mathematics and Statistics 45, sy. 2 (Nisan 2016): 521-40.
EndNote A. Corzo J, Vergara ME (01 Nisan 2016) A data driven runs test to identify first order positive Markovian dependence. Hacettepe Journal of Mathematics and Statistics 45 2 521–540.
IEEE J. A. Corzo ve M. E. Vergara, “A data driven runs test to identify first order positive Markovian dependence”, Hacettepe Journal of Mathematics and Statistics, c. 45, sy. 2, ss. 521–540, 2016.
ISNAD A. Corzo, Jimmy - Vergara, Myrian E. “A Data Driven Runs Test to Identify First Order Positive Markovian Dependence”. Hacettepe Journal of Mathematics and Statistics 45/2 (Nisan 2016), 521-540.
JAMA A. Corzo J, Vergara ME. A data driven runs test to identify first order positive Markovian dependence. Hacettepe Journal of Mathematics and Statistics. 2016;45:521–540.
MLA A. Corzo, Jimmy ve Myrian E. Vergara. “A Data Driven Runs Test to Identify First Order Positive Markovian Dependence”. Hacettepe Journal of Mathematics and Statistics, c. 45, sy. 2, 2016, ss. 521-40.
Vancouver A. Corzo J, Vergara ME. A data driven runs test to identify first order positive Markovian dependence. Hacettepe Journal of Mathematics and Statistics. 2016;45(2):521-40.