Choosing Which Distribution to Use
The most common probability distributions are thenormal, binomial, poisson, geometric and uniform distributions. Eachcan be used to model certain situations,and if approximations are allowed, more than one model is possiblefor any given situation. The normal distribution, can for example beused an as an approximation for any distribution under certaincircumstance, because of the Central Limit Theorem.
The Normal Distribution – can be used to modelsymmetric bell shaped distributions. It cannot be theoretically usedto model a distribution if there are restrictions on the values thedistribution may take. For example, we cannot theoretically use it tomodel the lengths of snails, because there exists a lower limit of 0,but in practice the normal distribution is often used to model suchsituations. The normal distribution can be either a continuous, orusing the continuity correction, discrete distribution.
The Binomial Distribution – can be used in anysituation where the probability of success is fixed. The binomialdistribution models the number of successes in n trial, where n is afixed number. The binomial distribution is a discrete distributionsince in n trials the number of successes is an integer.
The Poisson Distribution – can be used to model anydistribution where events happen at a certain rate per unit time, ormisprints happen on average at so many per page. Under somecircumspances, where p is small – less than-and n is large – greater than 30 - the Poisson distribution can beused as an approximation to the binomial distribution. The Poissondistribution is an integer since the number of events in each timeperiod is an integer.
The Geometric Distribution – used to model the numberof attempts until the first success. The probability p has to befixed so this distribution cannot be used to model learning games. The Geometric distribution is a discrete distribution, since thenumber of attempts must be an integer.
The Uniform Distribution. The probability of eachoutcome is the same. Theset of values that may be taken has finite upper and lower limits,meaning that any observed value must be between two numbers. Theuniform distribution can be either continuous or discrete.