Which is the best distribution to study the daily admission of head injury patients in a trauma care centre? (AIIMS Nov 2011)
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.
1. The distribution was discovered by Siméon-Denis Poisson .
2. The work focused on certain random variables N that count, among other things, a number of discrete occurrences (sometimes called "arrivals") that take place during a time-interval of given length
3. The Poisson distribution arises in connection with Poisson processes. It applies to various phenomena of discrete nature (that is, those that may happen 0, 1, 2, 3, ... times during a given period of time or in a given area) whenever the probability of the phenomenon happening is constant in time or space. Examples of events that may be modeled as a Poisson distribution include:
a. The number of cars that pass through a certain point on a road (sufficiently distant from traffic lights) during a given period of time.
b. The number of spelling mistakes one makes while typing a single page.
c. The number of phone calls at a call center per minute.
d. The number of times a web server is accessed per minute.
e. The number of road kill (animals killed) found per unit length of road.
f. The number of mutations in a given stretch of DNA after a certain amount of radiation.
g. The number of unstable nuclei that decayed within a given period of time in a piece of radioactive substance. The radioactivity of the substance will weaken with time, so the total time interval used in the model should be significantly less than the mean lifetime of the substance.
h. The number of pine trees per unit area of mixed forest.
i. The number of stars in a given volume of space.