biostatistics and research methodology Possoins distribution.pptx

Poission Distribution

1. POISSON DISTRIBUTION Shaikh Sabina Meraj Assistant Professor Y B Chavan College of Pharmacy

2. There are situations in which the number of times an event occurs can be counted but the number of times the event did not occur cannot be counted. Actually the latter would be meaningless. For example, 1. the amount of radioactive fallouts during a certain duration, following a nuclear explosion can be measured and it is meaningless to think of the amount of nuclear dust that has not fallen during this period. 2. The number of goals scored by a football team in a series of matches can be counted but not the number of goals not scored. 3. The number of spells of diarrhoea observed in a group of infants over a predetermined period can be counted hit not the number of spells that did not occur. The probability of observing one spell, two spells etc , in a given sample in such cases, can be theoretically found out by the use of Poisson distribution.

3. Poison distribution is a discrete probability distribution and is used very widely in physical and social sciences. It was discovered by the French mathematician and physicist Simeon Denis Poison (1781-1840) who published it in 1837.

4. Binomial probability distribution gives an idea of the probability of getting a specific number of occurrences in a given number of trials. However, this distribution studies the probabilities of rare events which are common in science. For example, the emission of particles from a radioactive source, persons dying due to a rare disease, the number of typing mistakes committed by a good typist etc. are rare events, in the sense that the probability of their happening is very rare. In view of this, the Poisson distribution is extensively used in the fields of biology and medicine.

5. Poison distribution is a limiting case of the binomial distribution under the following conditions: ( i ) n, the number of trials is indefinitely large, i.e., n. ⏦. (ii) p, the constant probability of success for each trial is indefinitely small, i.e., p 0 (iii) np =   λ (say) is finite. Thus p = λ / n, q = 1 - λ / n, where λ is a positive real number.

6. Definition: A random variable X is said to follow a Poison distribution if it assumes only non-negative values and its probability mass function is given by P(X=x) = e - λ λ x . X = 0,1,2,3...... x! Here λ is known as the parameter of the distribution and λ > 0. We shall use the notation X ~ P( λ ) to denote that X is a Poisson variate with parameter λ .

7. Properties of Poison Distribution Poisson distribution has only one parameter ' λ ‘. Mean of a Poisson distribution is ' λ '. Variance of a Poisson distribution is λ This is the only distribution of where the mean and the variance are equal. Standard deviation is .  

8. Following are some instances where Poison distribution may be successfully employed Number of deaths from a disease (not in the form of an epidemic) such as heart attack or cancer or due to snake bite. Number of suicides reported in a particular city. Number of plane accidents per week. umber of defective item in a box of 100 items, manufactured by a good concern. Number of faulty blades in a packet of 100. Number of telephone calls received at a particular telephone exchange in some unit of time or connections to wrong number in a telephone exchange. Number of printing mistakes at each page of the book, committed by a good typist. The emission of radioactive (alpha) particles. The number of fragments received by a surface area 't from a fragment atom bomb.

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