The Bivariate Erlang and its Application in Modeling Recurrence Times of Kidney Dialysis Data

Norou Diawara; S.H. Sathish Indika; Melva Grant; Edgard M. Maboudou-Tchao

doi:10.6000/1929-6029.2014.03.02.2

The Bivariate Erlang and its Application in Modeling Recurrence Times of Kidney Dialysis Data

Authors

Norou Diawara Old Dominion University, 4700 Elkhorn Ave., Norfolk, VA 23529, USA
S.H. Sathish Indika Thomas Nelson Community College, 99 Thomas Nelson Drive, Hampton, VA 23666, USA
Melva Grant Old Dominion University, 4700 Elkhorn Ave., Norfolk, VA 23529, USA
Edgard M. Maboudou-Tchao University of Central Florida, 4000 Central Florida Blvd., Orlando, FL 32816, USA

DOI:

https://doi.org/10.6000/1929-6029.2014.03.02.2

Keywords:

Bivariate models, Erlang, exponential, Dirac delta

Abstract

Recent advances in computer modeling allows us to find closer fits to data. Our emphasis is on the interdependence between occurrence at kidney dialysis. The interdependence between kidney dialysis occurrences is modelled by a bivariate exponential that we propose in this article. The application is shown on the McGilchrist and Aisbett kidney data set with the use of the exponential distribution. The proposed bivariate exponential model has exponential marginal densities, correlated via a latent random variables and with finite probability of simultaneous occurrence. Extension of the model to a bivariate Erlang type distribution with same shape parameter is presented.

References

Marshall AW, Olkin I. A Multivariate Exponential Distribution. J Am Stat Assoc 1967; 63: 30-44. http://dx.doi.org/10.1080/01621459.1967.10482885 DOI: https://doi.org/10.1080/01621459.1967.10482885

Coresh J, Selvin E, Stevens LA, et al. Prevalence of Chronic Kidney Disease in the United States. J Am Med Assoc 2007; 298(17): 2038-47. http://dx.doi.org/10.1001/jama.298.17.2038 DOI: https://doi.org/10.1001/jama.298.17.2038

Harris A, Cooper BA, Jing Li J, et al. Cost-Effectiveness of Initiating Dialysis Early: A Randomized Controlled Trial. Am J Kidney Diseases 2011; 57(5): 707-15. http://dx.doi.org/10.1053/j.ajkd.2010.12.018 DOI: https://doi.org/10.1053/j.ajkd.2010.12.018

Csorgo S, Welsh AH. Testing for Exponential and Marshall-Olkin Distributions. J Stat Plan Infer 1989; 23; 287-300. http://dx.doi.org/10.1016/0378-3758(89)90073-6 DOI: https://doi.org/10.1016/0378-3758(89)90073-6

Zhao P, Balakrishnan N. Ordering Properties of Convolutions of heterogeneous Erlang and Pascal Random Variables. Stat Probability Lett 2010; 80: 969-74. http://dx.doi.org/10.1016/j.spl.2010.02.010 DOI: https://doi.org/10.1016/j.spl.2010.02.010

Iyer SK, Manjunath D. Correlated Bivariate Sequence for queueing and reliability applications. Commun Stat 2004; 33: 331-50. http://dx.doi.org/10.1081/STA-120028377 DOI: https://doi.org/10.1081/STA-120028377

Iyer SK, Manjunath D, Manivasakan R. Bivariate Exponential Distributions Using Linear Structures. Sankhya 2002; 64(A): 156-66.

McGilchrist CA, Aisbett CW. Regression with Frality in Survival Analysis. Biometrics 1991; 47; 461-66. http://dx.doi.org/10.2307/2532138 DOI: https://doi.org/10.2307/2532138

Abramowitz M, Stegun IA. Handbook of Mathematical Functions, Selected Government Publications, Chapter 6, New York, Dover 1972.

Hougaard P. A class of multivariate failure time distributions. Biometrika 1986; 73(3): 671-78. DOI: https://doi.org/10.1093/biomet/73.3.671

http://www.dx.doi.org/10.1093/biomet/73.3.671

Pickands J. Multivariate Extreme Value Distributions. Bull Int Stat Instit 1981; 49: 859-78.

Johnson RA, Evans JW, Green DW. Some Bivariate Distributions for Modeling the strength properties of Lumber 1999; US Department of Agriculture, Forest Service, Forest Products laboratory, Res. Pap. pp. 11.

Diawara N, Indika SHS, Maboudou-Tchao EM. The Distribution of the Sum of Independent Product of Bernoulli and Exponential. Am J Math Manag Sci 2013; 32(1): 75-89.

Carpenter M, Diawara N, Han Y. A New Class Of Bivariate Survival and Reliability Models. Am J Math Manag Sci 2006; 26: 163-84. DOI: https://doi.org/10.1080/01966324.2006.10737665

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Published

2014-04-30

How to Cite

Diawara, N., Indika, S. S., Grant, M., & Maboudou-Tchao, E. M. (2014). The Bivariate Erlang and its Application in Modeling Recurrence Times of Kidney Dialysis Data. International Journal of Statistics in Medical Research, 3(2), 88–93. https://doi.org/10.6000/1929-6029.2014.03.02.2

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Issue

Vol. 3 No. 2 (2014)

Section

General Articles

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