Page 299 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 14.3 Summary

This Poisson distribution was derived by a noted mathematician, Simon D. Poisson, in
1837.
This distribution was derived as a limiting case of binomial distribution,

When the number of trials n tends to become very large and the probability of success in
a trial p tends to become very small such that their product np remains a constant.

This distribution is used as a model to describe the probability distribution of a random
variable defined over a unit of time, length or space.

The number of telephone calls received per hour at a telephone exchange, the number of
accidents in a city per week, the number of defects per meter of cloth, the number of
insurance claims per year, the number breakdowns of machines at a factory per day, the
number of arrivals of customers at a shop per hour, the number of typing errors per page
etc. all are examples of poisson distribution
To fit a Poisson distribution to a given frequency distribution, we first compute its
mean m.
The range of the random variable is 0 r < .

The Poisson distribution is a positively skewed distribution. The skewness decreases as m
increases.

This distribution is applicable to situations where the number of trials is large and the
probability of a success in a trial is very small.

It serves as a reasonably good approximation to binomial distribution when n 20 and
p 0.05 .

14.4 Keywords

Poisson Approximation to Binomial: Poisson distribution can be used as an approximation to
binomial with parameter m = np.

Poisson Distribution: This is a a limiting case of binomial distribution, when the number of
trials n tends to become very large and the probability of success in a trial p tends to become
very small such that their product np remains a constant. This distribution is used as a model to
describe the probability distribution of a random variable defined over a unit of time, length or
space.
Poisson Process: Using symbols, we may note that as n increases then p automatically declines
in such a way that the mean m (= np) is always equal to a constant. Such a process is termed as a
Poisson Process.

Probability Mass Function: The probability mass function (p.m.f.) of Poisson distribution can
be derived as a limit of p.m.f. of binomial distribution when n such that m (= np) remains
constant.

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