|
|
Poisson Approximations
Klikáč, Jan ; Omelka, Marek (advisor) ; Kulich, Michal (referee)
This bachelor thesis deals with the counting probability using Poisson distri- bution and shows new ways of approximating Poisson distribution. The first chapter summarizes the findings regarding the Poisson distribution, its definition and properties. It also show a limit transition from the binomial distribution to Poisson distibution and examples demonstrating the usage of this limit transition. Brun Sieve is introduced in the second chapter. It gives a new possibility of transiting to a Poisson distribution. Random variables, which we want to appro- ximate, no longer need to have binomial distribution. Instead the property of expected value is required. The second part of the chapter includes a practical demonstration of the usage of Brun Sieve. In the third chapter we estimate size of the error that we made when approxi- mating to Poisson distribution. There is also formulated Stein-Chen theorem for estimating the error of Poisson approximation and its version for a special case. Keywords: Poisson distribution, Brun Sieve, Stein-Chen theorem 1
|
|
| |
|
|
Poisson Approximations
Klikáč, Jan ; Omelka, Marek (advisor) ; Kulich, Michal (referee)
This bachelor thesis deals with the counting probability using Poisson distri- bution and shows new ways of approximating Poisson distribution. The first chapter summarizes the findings regarding the Poisson distribution, its definition and properties. It also show a limit transition from the binomial distribution to Poisson distibution and examples demonstrating the usage of this limit transition. Brun Sieve is introduced in the second chapter. It gives a new possibility of transiting to a Poisson distribution. Random variables, which we want to appro- ximate, no longer need to have binomial distribution. Instead the property of expected value is required. The second part of the chapter includes a practical demonstration of the usage of Brun Sieve. In the third chapter we estimate size of the error that we made when approxi- mating to Poisson distribution. There is also formulated Stein-Chen theorem for estimating the error of Poisson approximation and its version for a special case. Keywords: Poisson distribution, Brun Sieve, Stein-Chen theorem 1
|
|
| |
guest ::
