Revelation of shrunken or stretched binomial dispersion and public perception of situations which might spread AIDS or HIV

Ramalingam Shanmugam


Background:In 1985, the center for disease control coined the name: “Acquired Immune Deficiency Syndrome (AIDS)” to refer a deadly illness. The World Health Organization (WHO) estimated that about 33.4 million people were suffering with AIDS and two million people (including 330,000 children) died in 2009 alone in many parts of the world. A scary fact is that the public worry about situations which might spread AIDS according to reported survey result in Meulders et al. (2001). This article develops and illustrates an appropriate statistical methodology to understand the meanings of the data.

Methods: While the binomial model is a suitable underlying model for their responses, the data mean and dispersion violates the model’s required functional balance between them. This violation is called over-under dispersion. This article creates an innovative approach to assess whether the functional imbalance is too strong to reject the binomial model for the data. In a case of rejecting the model, what is a correct way of warning the public about the spreads of AIDS in a specified situation? This question is answered.

Results: In the survey data about how AIDS/HIV might spread according to fifty respondents in thirteen nations, the functional balance exists only in three cases: “needle”, “blood” and “sex” justifying using the usual binomial model (1). In all other seven cases: “glass”, “eating”, “object”, “toilet”, “hands”, “kissing”, and “care” of an AIDS or HIV patient, there is a significant imbalance between the dispersion and its functional equivalence in terms of the mean suggesting that the new binomial called imbalanced binomial distribution (6) of this article should be used. The statistical power of this methodology is indeed excellent and hence the practitioners should make use of it.  

Conclusion:The new model called imbalanced binomial distribution (6) of this article is versatile enough to be useful in other research topics in the disciplines such as medicine, drug assessment, clinical trial outcomes, business, marketing, finance, economics, engineering and public health.



Over/under dispersion, Ratio of statistics, p-value, Statistical power, Hypothesis test, Nuisance parameter

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CDC. Revision of the case definition of acquired immunodeficiency syndrome for national reporting in the United States. Morb Mortal Weekly Rep. 1985;34:373-5.

Meulders M, Boeck PD, Mechelen IV, Gelman A, Maris E. Bayesian inference with probability matrix decomposition models. J Edu Behavioural Stat. 2001;26:153-79.

Shanmugam R. An inferential procedure for the Poisson intervention parameter. Biometrics. 1992;48:559-65.

Stuart A. K. Ord Kendal. In: Stuart A. K., J. Keith, eds. Kendall’s Advanced Theory of Statistics. 1st ed. London U. K.: Griffin Publication; 2009: 356-359.