Poisson Distribution Part I

The normal distribution is symmetric and is used to approximate the binomial distribution when p = q = 1/2. When p is very small, then the resulting distribution is not symmetric as the number of trials becomes large. When n, the number of trials is large and p is very small we approximate the binomial distribution with the Poisson distribution.

The Poisson distribution is used when the probability of success is very small. The probability of a mutation is very small. The probability of a double-cross over is small. Haldane and Kosambi used the Poisson distribution to adjust the observed number of crossover events to the map distance. Map distance is the physical distance between loci on a chromosome and is not the same as the recombination proportion. A characteristic of the Poisson distribution is that the population mean and variance are equal. We will use the Poisson distribution later when we discuss mapping functions.

Let m = the mean number of successful events. The probability of x successful events is given by the formula.