Poisson distribution is a discrete probability distribution that describes the probability of an event happening in a fixed time interval. Historically, it has been used in various ways (Shanker & Fesshaye, 2017). One of the popular applications of the poison distribution is the simulating deaths by horse kick of Prussian cavalry soldiers by Ladislaus Bortkiewicz. In this study, poison probability was used because the event of death happens in a specified or fixed time interval. There is a probability of success, which is death and average time deaths. Further, it explains the theoretical probability of a death event. The death of horses is rare among individuals who spent most of the time with horses. Thus, the poison probability predicted the number of deaths since they were rare. This is why the theoretical probability is high when the number of deaths is zero for all events. It estimated the total expected deaths for all corps years that are very close to what is observed ( Shanker & Fesshaye, 2017 ). For this reason, Bortkiewicz believed that the deaths of horses can be estimated using the poison distribution among Prussian cavalry soldiers.
The poison probability cannot be used to compute the probability of winning the contest or finishing. We will use the standard normal tables to find the z score for the percentile. From the Z tables, the z score for the 1% percentile is greater compared to -2.326. Therefore, the probability that the Z score is greater than -2.326 will be 0.9898. It is compared as follows, P ( Z > -2.32) = 1 – p ( z < -2.32) = 1 – 0.01017 = 0.98983. Hence, the probability that I will top in 1% will be 0.98983 (98.983 %). Thus, the Poisson probability will not be used.
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Reference
Shanker, R., & Fesshaye, H. (2017). On discrete Poisson-Shanker distribution and its applications. Biom Biostat Int J , 5 (1), 00121.
