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Unified Survival Functions are Derived and Illustrated Using Hospitals’ Preparedness Data to Treat Anthrax Cases

Ramalingam Shanmugam


This article is the first of its kind to show how survival function of popular distributions such as binomial, Poisson, and inverse binomial can be derived in a unified manner using a Taylor’s series expansion. Consequently, their survival functions are expressed in terms well publicized chi-squared or F distributions whose tail areas are extensively tabulated. The expressions are useful to hospital administrators in many countries including the United States of America (USA) are pointed out. The hospitals are expected to treat effectively and quickly the anthrax inflicted patients due to a bio-terrorized act. In this respect, the Center for Disease Control (CDC) in the USA conducted a survey to assess how prepared are the hospitals to effectively treat anthrax cases. The hospitals target zero-casualty among anthrax inflicted patients in their treatment. Using the CDC’s data and the newly derived expressions of this article, an answer is developed to the question: how similar or different are the states in four time zones of USA in the preparedness to treat anthrax patients due to any bioterrorism?


Binomial, inverse binomial, Poisson, exponential, chi-squared and F distributions, cumulative distribution, mean exponential family, Taylor series.

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