Marshall and Olkin’s Distributions

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Baxter, L.A., Rachev, S.T.: The stability of a characterization of the bivariate Marshall–Olkin distribution. J. Math. Anal. Appl. 160, 563–571 (1991)

Beg, M.I., Balasubramanian, K.: Concomitant of order statistics in the bivariate exponential distributions of Marshall and Olkin. Calcutta Stat. Assoc. Bull. 46, 109–115 (1996)

Begum, A.A., Khan, A.H.: Concomitants of order statistics from Marshall and Olkin’s bivariate Weibull distribution. Calcutta Stat. Assoc. Bull. 50, 65–70 (2000)

Boland, P.J.: An arrangement increasing property of the Marshall–Olkin bivariate exponential. Stat. Probab. Lett. 37, 167–170 (1998)

Csörgö, S., Welsh, A.H.: Testing for exponential and Marshall–Olkin distributions. J. Stat. Plann. Inference 23, 287–300 (1989)

Ebrahimi, N.: Analysis of bivariate accelerated life test data for the bivariate exponential distribution. Am. J. Math. Manag. Sci. 7, 175–190 (1987)

El-Gohary, A., Sarhan, A.: The distributions of sums, products, ratios and differences for Marshall–Olkin bivariate exponential distribution. Int. J. Appl. Math. 20, 351–370 (2007)

Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher Transcendental Functions, vol. 1. Krieger, New York (1981)

Falk, M., Reiss, R.-D.: A characterization of the Marshall–Olkin dependence function and a goodness-of-fit test. Sankhyā 65, 807–820 (2003)

Filus, J.K.: Some modifications of the multidimensional Marshall and Olkin model. Int. J. Syst. Sci. 21, 1145–1152 (1990)

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Jana, P.K.: Estimation for P[Y<X] in the bivariate exponential case due to Marshall and Olkin. J. Indian Stat. Assoc. 32, 35–37 (1994)

Jeevanand, E.S.: Bayes estimation of reliability under stress–strength model for the Marshall–Olkin bivariate exponential distribution. IAPQR Trans. 23, 133–136 (1998)

Kakosyan, A.V.: On an estimate for the closeness of a two-dimensional distribution with a monotonically increasing failure rate function to the Marshall–Olkin distribution. Sov. J. Contemp. Math. Anal. 24, 100–102 (1989)

Kim, D.H., Cho, K.H., Cho, J.S.: Bootstrap testing for independence in Marshall and Olkin’s model under random censorship. Korean J. Appl. Stat. 9, 13–23 (1996)

Klefsjö, B.: NBU and NBUE survival under the Marshall–Olkin shock model. IAPQR Trans. 7, 87–96 (1982)

Kopocińska, I.: Bivariate negative binomial distribution of the Marshall–Olkin type. Appl. Math. 25, 457–461 (1999)

Marshall, A.W., Olkin, I.: A multivariate exponential distribution. J. Am. Stat. Assoc. 62, 30–44 (1967)

Marshall, A.W., Olkin, I.: A family of bivariate distributions generated by the Bernoulli distribution. J. Am. Stat. Assoc. 80, 332–338 (1985)

Marshall, A.W., Olkin, I.: Adding a parameter to a family of distributions. Biometrika 84, 641–652 (1997)

Mitov, K.V., Nadarajah, S.: Limit distributions for the bivariate geometric maxima. Extremes 8, 357–370 (2005)

Muliere, P., Scarsini, M.: Characterization of a Marshall–Olkin type class of distributions. Ann. Inst. Stat. Math. 39, 429–441 (1987)

Nadarajah, S., Kotz, S.: Sums and ratios for Marshall and Olkin’s bivariate exponential distribution. Math. Sci. 30, 112–119 (2005)

Obretenov, A.: Characterization of the multivariate Marshall–Olkin exponential distribution. Probab. Math. Stat. 6, 51–56 (1985)

Obretenov, A., Rachev, S.: Characterizations of the bivariate exponential distribution and Marshall–Olkin distribution and stability. In: Stability Problems for Stochastic Models, Moscow, 1982. Lecture Notes in Mathematics, vol. 982, pp. 136–150. Springer, Berlin (1983)

Osaki, S.: A two-unit parallel redundant system with bivariate exponential lifetimes. Microelectron. Reliab. 20, 521–523 (1980)

Osaki, S., Yamada, S., Hishitani, J.: Availability theory for two-unit nonindependent series systems subject to shut-off rules. Reliab. Eng. Syst. Saf. 25, 33–42 (1989)

Pena, E.A., Gupta, A.K.: Bayes estimation for the Marshall–Olkin exponential distribution. J. R. Stat. Soc. B 52, 379–389 (1990)

Rai, K., Van Ryzin, J.: Multihit models for bivariate quantal responses. Stat. Decis. 2, 111–129 (1984)

Ramanarayanan, R., Subramanian, A.: A 2-unit cold standby system with Marshall-Olkin bivariate exponential life and repair times. IEEE Trans. Reliab. R-30, 489–490 (1981)

Ryu, K.: An extension of Marshall and Olkin’s bivariate exponential distribution. J. Am. Stat. Assoc. 88, 1458–1465 (1993)

Sugasaw, Y., Kaji, I.: Light maintenance for a two-unit parallel redundant system with bivariate exponential lifetimes. Microelectron. Reliab. 21, 661–670 (1981)

Thomas, A., Jose, K.K.: Marshall–Olkin Pareto processes. Far East J. Theor. Stat. 9, 117–132 (2003)

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Volodin, N.A., Shukurlaeva, S.K.: Rate of convergence of random sums of random vectors to Marshall–Olkin distribution. Stability problems for stochastic models. J. Sov. Math. 47, 2681–2684 (1989)

Wu, C.: New characterization of Marshall–Olkin–type distributions via bivariate random summation scheme. Stat. Probab. Lett. 36, 171–178 (1997)

Yeh, H.-C.: The generalized Marshall–Olkin type multivariate Pareto distributions. Commun. Stat. Theory Methods 33, 1053–1068 (2004)