An Application of Discrete Probability Models to the Number of Outpatient Visits

1985 ◽  
Vol 26 (2) ◽  
pp. 159
Author(s):  
Han Joong Kim ◽  
Dong Kee Kim ◽  
Il Soon Kim
Keyword(s):  
Probability Models ◽  
Discrete Probability ◽  
Outpatient Visits

scholarly journals Correcting for Non-Sum to 1 Estimated Probabilities in Applications of Discrete Probability Models to Count Data

2017 ◽  
Vol 6 (5) ◽  
pp. 119
Author(s):  
Bayo H. Lawal
Keyword(s):  
Sample Size ◽  
Count Data ◽  
Negative Binomial ◽  
Frequency Count ◽  
Frequency Data ◽  
Probability Models ◽  
Common Procedure ◽  
Discrete Probability ◽  
Excess Zeros ◽  
Expected Values

In this paper, we examine some often ignored or assumed problems relating with fitting probability models to count data either exhibiting over, equi, or under dispersion. Of particular concern are last category truncated data, where most often, expected values in this last category are collapsed together so that the sum of the expected values sum to the sample size in the data. That is, so that $\displaystyle \sum_{i=0}^{k} \hat{m}_i=n$, the sample size. We shall for illustrative purposes in this paper, consider the following distributions: the negative binomial (NB), the Inverse trinomial (IT), the hyper-Poisson (HP), the Quasi-negative binomial (QNBD), the extended com-Poisson distribution (ECOMP) as well as the negative binomial-exponential distribution (NBGE).Though, we have restricted our discussion to these six distributions, other distributions may also be employed but the patterns are always the same, that is, the sum of the estimated probabilities does not equal 1.00 and consequently, the sum of the expected values is always less or equal (Poisson case only) the sample size in the observed data. We propose a common procedure to rectify this problem for both right truncated or non-truncated frequency count data exhibiting either excess zeros or regular frequency data.

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