The Poisson distribution is a discrete probability distribution that depends on one parameter, m If X is a random variable with the Poisson distribution with parameter m, then the probability that X = k is
Poisson distributions model (some) discrete random variables Typically, a Poisson random variable is a count of the number of events that occur in a certain time interval or spatial area For example, the number of cars passing a fixed point in a five minute interval
A one-parameter discrete frequency distribution giving the probability the n points (or events) will be (or occur) in an interval (or time) x , provided that these points are individually independent and that the number occurring in a subinterval does not influence the number occurring in any other nonoverlapping subinterval It has the form f(n,x) = e-σx(σx)n/n! The mean and variance are both σx , and σ is the average density (or rate) with which the events occur When σx is large, the Poisson distribution approaches the normal distribution The binomial distribution approaches the Poisson when the number of events n becomes large and the probability of success P becomes small in such a way that nP aproaches σx
A distribution often used to express probabilities concerning the number of events per unit For example, the number of computer malfunctions per year, or the number of bubbles per square yard in a sheet of glass, might follow a Poisson distribution The distribution is fully characterized by its mean, usually expressed in terms of a rate Parameters: mean B>0 Domain: X=0,1,2, Mean: B Variance: B
A poisson distribution is a distribution of random occurrences in which one occurrence has no influence on any other occurrence The variance of a poisson distribution is equal to its mean and therefore the standard deviation is equal to the square root of the mean of the distribution Radioactive decay measurements follow a poisson distribution and therefore have a lower measurement error when more counts are accumulated
A discrete distribution applicable when the probability of an event happening within a very small time period, is a very small number, the probability that two or more such events will occur within the same time interval is almost zero and the probability of the occurrence of the event within one time period is independent of where that time period is
A statistical tool that assumes 3 conditions: for any one observation only two results are possible; the chances of these two results do not vary from one observation to the next; and successive observations are independent
A probability distribution that characterizes discrete events occurring independently of one another in time Probabilistic earthquake hazard See Earthquake hazard and Earthquake risk
a mathematical formula that used to be used in traffic engineering for calculating the probability of blocked calls in a telephone network; now we have CTI software that provides graphs of trunk groups and their usage