Modeling Discrete Bivariate Data with Applications to Failure and Count Data

Quality and Reliability Engineering International

Volumn 33, Issue 7, 2017, Pages 1455-1473

  Lee, Hyunju ^a   Cha, Ji Hwan ^a   Pulcini, Gianpaolo ^b  

^a Ewha Womans University   (South Korea)

^b ISTITUTO MOTORI CNR   (Italy)

Author keywords

count data; discrete survival data; discrete time failure rate function; negative dependence; proportional hazard type modeling

Indexed keywords

COPYRIGHTS; FAILURE ANALYSIS; RANDOM VARIABLES;

COUNT DATUM; FAILURE RATE FUNCTIONS; NEGATIVE DEPENDENCE; PROPORTIONAL HAZARDS; SURVIVAL DATA;

POISSON DISTRIBUTION;

EID: 85019502118     PISSN: 07488017     EISSN: 10991638     Source Type: Journal    
DOI: 10.1002/qre.2118     Document Type: Article

References (30)

1. Holgate B. Estimation for the bivariate Poisson distribution. Biometrika 1964; 51(1/2):241–245.
2. Block HW, Basu AP. A continuous bivariate exponential extension. Journal of the American Statistical Association 1974; 69(348):1031–1037.
3. Freund JE. A bivariate extension of the exponential distribution. Journal of the American Statistical Association 1961; 56(296):971–977.
4. Lee H, Cha JH. On construction of general classes of bivariate distributions. Journal of Multivariate Analysis 2014; 127:151–159.
5. Marshall AW, Olkin I. A multivariate exponential distribution. Journal of the American Statistical Association 1967; 62(317):30–44.
6. Hougaard P. Modeling multivariate survival. Scandinavian Journal of Statistics 1987; 14(4):292–304.
7. Balakrishnan N, Lai C. Continuous Bivariate Distributions (2nd edn). Springer: New York, 2009.
8. Basu AP, Dhar SK. Bivariate geometric distribution. Journal of Applied Statistical Science 1995; 2(12):33–34.
9. Campbell JT. The Poisson correlation function. Proceedings of the Edinburgh Mathematical Society, Series 2 1934; 4:18–26.
10. Dhar SK. Data analysis with discrete analogue of Freund's model. Journal of Applied Statistical Science 1998; 7:169–183.
11. Kocherlakota S. Discrete bivariate weighted distributions under multiplicative weight function. Communications in Statistics – Theory and Methods 1995; 24(2):533–551.
12. Lee H, Cha JH. On two general classes of discrete bivariate distributions. The American Statistician 2015; 69(3):221–230.
13. Mishra A. A generalised bivariate binomial distribution applicable in four-fold sampling. Communications in Statistics – Theory and Methods 1996; 25(8):1943–1956.
14. Nekoukhou V, Alamatsaz MH, Bidram H. Discrete generalized exponential distribution of a second type. Statistics 2013; 47(4):876–887.
15. Nikulin MS, Smirnov TI, Voinov VG. Multivariate discrete distributions induced by an urn scheme, linear diophantine equations, unbiased estimating, testing and applications. Journal of Statistical Planning and Inference 2002; 101(1–2):255–266.
16. Ong SH, Ng CM. A bivariate generalization of the noncentral negative binomial distribution. Communications in Statistics: Simulation and Computation 2013; 42(3):570–585.
17. Kocherlakota S, Kocherlakota K. Bivariate Discrete Distributions. Marcel and Dekker. Inc: New York, 1992.
18. Johnson NL, Kotz S, Balakrishnan N. Discrete Multivariate Distributions. Wiley: New York, 1997.
19. Karlis D, Ntzoufras I. On modeling soccer data. Student 2000; 3(4):229–244.
20. Lee AJ. Modeling scores in the Premier League: is Manchester United really the best? Chance 1997; 10(1):15–19.
21. Maher MJ. Modeling association football scores. Statistica Neerlandica 1982; 36(3):109–118.
22. Morata LB. A priori ratemaking using bivariate Poisson regression models. Insurance: Mathematics and Economics 2009; 44(1):135–141.
23. Wu X, Yuen KC. A discrete-time risk model with interaction between classes of business. Insurance: Mathematics and Economics 2003; 33(1):117–133.
24. Yuen KC, Guo J, Wu X. On the first time of ruin in the bivariate compound Poisson model. Insurance: Mathematics and Economics 2006; 38(2):298–308.
25. Aitchison J, Ho CH. The multivariate Poisson-log normal distribution. Biometrika 1989; 76(4):643–653.
26. ReliaSoft's R&D staff. Using QALT models to analyze system configurations with load sharing. Reliability Edge 2002; 3:1–4.Available: http://www.reliasoft.com/pubs/reliabilityedge_4q2002.pdf
27. Roy D, Gupta R. Classification of discrete lives. Microelectronics Reliability 1992; 32(10):1459–1473.
28. Johnson NL, Kemp AW, Kotz S. Univariate Discrete Distributions (3rd edn). Wiley: New Jersey, 2005.
29. Lawless JF. Statistical Models and Methods for Lifetime Data. John Wiley and Sons: New York, 1982.
30. Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control 1974; 19(6):716–723.