Abstract
Marshall–Olkin semi-Burr and Marshall–Olkin Burr distributions are introduced and studied. Their various characteristics in reliability analysis are derived. Applications in time series analysis are discussed.
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Alice T, Jose KK (2003) Marshall Olkin Pareto process. Far East J Theor Stat 9:117–132
Balakrishna N, Jayakumar K (1997) Bivarite semi-Pareto distributions and processes. Stat Pap 38:149–165
Burr IW (1942) Cumulative frequency functions. Ann Math Stat 13:215-232
Burr IW, Cislak PJ (1968) On a general system of distributions: I. Its curve-shaped characteristics; II. The sample median. J Am Stat Assoc 63:627–635
Ebrahimi N (1996) How to measure uncertainty in the residual life time distribution. Sankhya A 58:48–56
Hossain AM, Nath SK (1997) Estimation of parametersin the presence of Outliers for a Burr XII distribution. Commun Stat Theory Methods 26:637–652
Jayakumar K (1995) The stationary solution of a first order integer valued autoregressive process. Statistica LV:221–228
Jayakumar K (1997) First order autoregressive semi-α-Laplace process. Statistica LVII:455–463
Jayakumar K, Pillai RN (1993) The first order autoregressive Mittag-Leffler process. J Appl Probab 30:462–466
Jayakumar K, Thomas M (2002) Burr processes. Far East J Theor Stat 8:99–113
Kagan AM, Linnik Yu V, Rao CR (1973) Characterization problems in mathematical statistics. Wiley, New York
Lawrance AJ (1991) Directionality and reversibility in time series. Int Stat Rev 59:67–79
Marshall AW, Olkin I (1997) A new method for adding a parameter to a family of distributions with applications to exponential and Weibull families. Biometrika 84:641–652
Rodriguez N (1977) A guide to the Burr type XII distributions. Biometrika 64:129–134
Tadikamalla PR (1980) A look at the Burr and related distributions. Int Stat Rev 48:337–344
Tavares LV (1980) An exponential Markovian stationary process. J Appl Probab 17:1117–1120
Yao W, Hossain AM, Zimmer WJ (2003) Monotone log odds rate distribution in reliability analysis. Commun Stat Simul Comput 32:2227–2244
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Jayakumar, K., Mathew, T. On a generalization to Marshall–Olkin scheme and its application to Burr type XII distribution. Statistical Papers 49, 421–439 (2008). https://doi.org/10.1007/s00362-006-0024-5
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DOI: https://doi.org/10.1007/s00362-006-0024-5