Random spatial distribution is simulated using poisson distribution.

Simplest example: 100 people are fishing in the same lake for the same time (e.g. 3 h); they have equal probability to catch a fish per unit time. Question: How many fishers catch 0, 1, 2, 3 etc. fish?

No. of fish captured, i |
No. of fishers n(i) |
Proportion of fishers p(i) |
Poisson distribution n'(i)=Np'(i) |

0 |
11 |
0.11 |
10 |

1 |
25 |
0.25 |
23 |

2 |
21 |
0.21 |
27 |

3 |
25 |
0.25 |
20 |

4 |
9 |
0.09 |
12 |

5 |
7 |
0.07 |
5 |

6 |
2 |
0.02 |
2 |

7 |
0 |
0.00 |
1 |

Total |
N=100 |
1.00 |
100 |

Mean number of fish captured by 1 fisher, M = 2.30, and standard deviation, SD = 1.41. Poisson distribution is described by equation:

where m is the mean and i!= 1x2x3x ... xi, 0!=1; 1!=1. Theorem: In poisson distribution, mean = variance: m

Two main methods of parameter estimation

2. Non-linear regression (iterative approximation)

In the table above we used the method of moments: m = M = 2.3.

Chi-square test is used to test if sample distribution is different from theoretical distribution. The equation is:

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