Discrete distributions related to success runs of lengthk in aulti-state markov chain

References

• Aki , S. 1985 . Discrete distributions of order k on a binary sequence . Ann. Inst. Statist. Math , 37 ( A ) : 205 – 224 .
   Web of Science ®Google Scholar
• Aki , S. 1992 . Waiting time problems for a sequence of discrete random variables . Ann. Inst. Statist. Math , 44 ( A ) : 363 – 378 .
   Web of Science ®Google Scholar
• Aki , S. , Kuboki , H. and Hirano , K. 1984 . On discrete distributions of order k . Ann. Inst. Statist. Math , 36 ( A ) : 431 – 440 .
   Web of Science ®Google Scholar
• Aki , S. and Hirano , K. 1989 . Estimation of parameters in the discrete distributions of order k . Ann. Inst. Statist.Math , 41 ( A ) : 47 – 61 .
   Google Scholar
• Aki , S. , Hirano , K. , Puri , M. L. and Hayakawa , T. 1993 . “ Discrete distributions related to succession events in a two-state Markov chain ” . In Statistical Sciences and Data Analysis: Proceedings of the Third Pasific Area Statistical Conference , Edited by: Hayakawa , T. 467 – 474 . Zeist : VSP International Science Publishers .
   Google Scholar
• Aki , S. and Hirano , K. 1994 . Number of failures and successes until the first consecutive successes . Ann. Inst. Statist. Math , 46 : 193 – 202 .
   Google Scholar
• Aki , S. and Hirano , K. 1995 . Joint distributions of number of success runs and failures until the first consecutive k successes . Ann.Inst.Statist.Math , 47 : 225 – 235 .
   Google Scholar
• Balasubramanian , K. , Viveros , R. and Balakrishnan , N. 1993 . Sooner and later waiting time problems for Markovian Bernoulli trias . Statist. Probab.Lett , 18 : 153 – 161 .
   Web of Science ®Google Scholar
• Chaing , D. and Niu , S. C. 1981 . Reliability of con-secutive-fc-out-of n:F system . IEEE Transactions on Reliability , 30 April : 87 – 89 .
   Google Scholar
• Charalambides , A. 1986 . On discrete distributions of order k . Ann.Inst.Statist. Math , 38 April : 557 – 568 .
   Web of Science ®Google Scholar
• Ebneshahrashoob , M. and Sobel , M. 1990 . Sooner and later waiting time problems for Bernoulli trials: frequency and run quotas . Statist.Probab.Lett , 9 April : 171 – 175 .
   Google Scholar
• Feller , W. 1968 . An Introduction to Probability Theory and Its Applications Vol. 1 , New York, Wiley
   Google Scholar
• Hahn , G. J. and Gage , J. B. 1983 . Evaluation of a start-up demonstration test . Journal of Quality Tec-chnology , 15 : 103 – 106 .
   Web of Science ®Google Scholar
• Hirano , K. and Aki , S. 1993 . On number of occurrences of success runs of specified length in a two-state Markov chain . Statistica Sinica , 3 : 313 – 320 .
   Web of Science ®Google Scholar
• Kuotras , M. V. , Papadopoulos , G. K. and Papastavridis , S. G. 1995 . Runs on a circle . J. Appl. Probab , 32 : 396 – 404 .
   Google Scholar
• Ling , K. D. 1988 . Runs on a circle . J. Appl. Probab , 6 : 247 – 250 .
   Google Scholar
• Mohanty , S. G. 1994 . Success runs of length k in Markov dependent trials . Ann. Inst. Statist. Math , 46 : 777 – 796 .
   Web of Science ®Google Scholar
• Panaretos , J. and Xekalaki , E. 1986 . On some distri butions arising from certain generalized sampling schemes . Commun. Statist. - Theor. Meth , 15 : 873 – 891 .
   Web of Science ®Google Scholar
• Philippou , A. N. , Bergum , G. E. and Hordam , A. F. 1986 . “ Distributions and Fibonacci polinomials of order k, longest runs and reliability of consecutive-k-out-of n:F system ” . In Fibonacci Numbers and Their Applications Edited by: Hordam , A. F. 203 – 227 . Reidel, Dordrecht
   Google Scholar
• Philippou , A. N. 1988 . On multiparameter distributions of order k . Ann. Inst. Statist. Math , 40 : 467 – 475 .
   Web of Science ®Google Scholar
• Philippou , A. N. , Georghiou , C. and Philippou , G. N. 1983 . A generalized geometric distribution and some of its properties . Statist.Probab.Lett , 1 : 171 – 175 .
   Google Scholar
• Rajarshi , M. B. 1974 . Success runs in a two-state Markov chain . J. Appl. Probab , 11 : 190 – 192 .
   Google Scholar
• Sobel , M. and Ebneshahrashoob , M. 1992 . Quota sampling for multinomial via Dirichlet . Journ. Statist. Plann. Inference , 33 : 157 – 164 .
   Google Scholar
• Uchida , M. and Aki , S. 1995 . Sooner and later waiting time problems in a two-state Markov chain . Ann. Inst. Statist. Math , 47 : 415 – 433 .
   Google Scholar
• Viveros , R. and Balakrishnan , N. 1993 . Statisticalinference from start-up demonstration test data . Journal of Quality Control , 25 : 119 – 130 .
   Google Scholar
• Wetherill , G. B. and Brown , D. W. 1991 . Statistical Process Control: Theory and practice , Padstow, Cornwall : Chapman and Hall .
   Google Scholar