Abstract
Both Poisson and geometric distributions can be used quite effectively in modeling count data. In this paper we compare Bayesian and frequentists criteria to choose between Poisson and geometric distributions. In the frequentist choice, we use the ratio of maximized likelihood in discriminating between the two distributions. Asymptotic distributions of the ratio of maximized likelihoods are also obtained, and they can be used to compute the minimum sample size needed to discriminate between the two distributions. We further investigate the Bayesian model selection criterion in choosing the correct model, under a fairly general set of priors. We perform some simulation experiments to see the effectiveness of the proposed methods and the analysis of one data set is performed for illustrative purposes.
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References
Cox DR (1961) Tests of separate families of hypotheses. In: Proceedings of the 4th Berkeley symposium in mathematical statistics and probability, Berkeley, University of California Press, pp 105–123
Cox DR (1962) Further results on tests of separate families of hypotheses. J R Stat Soc Ser B 24:406–424
Dauxois J-Y, Druilhet P, Pommeret D (2006) A Bayesian choice between Poisson, binomial and negative binomial models. Test 15:423–432
Dumonceaux R, Antle CE (1973) Discriminating between the log-normal and Weibull distribution. Technometrics 15:923–926
Dey AK, Kundu D (2012) Discriminating between the Weibull and Log-normal distributions for type-II censored data. Statistics 46:197–214
Gupta RD, Kundu D (2003) Discriminating between Weibull and generalized exponential distributions. Comput Stat Data Anal 43:179–196
Kass RE, Raftery A (1995) Bayes factor. J Am Stat Assoc 90:769–781
Kundu D, Manglick A (2004) Discriminating between the Weibull and log-normal distributions. Naval Res Logist 51:893–905
Vu HTV, Muller RA (1996) The likelihood ratio test for Poisson versus binomial distributions. J Am Stat Assoc 91:818–824
White H (1982) Regularity conditions for Cox’s test of non-nested hypotheses. Econometrics 19:301–318
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Pradhan, B., Kundu, D. A Choice Between Poisson and Geometric Distributions. J Indian Soc Probab Stat 17, 111–123 (2016). https://doi.org/10.1007/s41096-016-0008-2
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DOI: https://doi.org/10.1007/s41096-016-0008-2