AGRI 2400 Lecture 12 - Distributions of Random Variables

Binomial Distribution

• observed for a discrete variable with only 2 possible outcomes where:

  • probability of those two outcomes is constant

  • each observation is indep.

  • appropriate when the probability of ‘success’ is not too small

Binomial Distribution Examples

• many instances of binomial distributions can be found in our fields of study

  • e.g. sex ratios of offspring in animal production systems

  • e.g. in herbicide trials, the product either kill the target weed or doesnt

  • presence or absence of parasites or pathogens in animals populations

Poisson Distribution

• variables exhibiting a Poisson distribution are those that record the discrete number of occurrences of an event recorded during a fixed area or interval of time (when occurrences are relatively rare)

  • e.g. the number of pests per quadrat

  • the number of flower visits by pollinators in 30 min throughout an afternoon

Poisson Distribution Observed When:

• the probability of “an event” is relatively small (rare)

• the mean value is small relative to the maximum (possible) observed value

• occurrences are indep. of one another

Spatial Patterns of Dispersion Matter

• not all discrete count data exhibits a Poisson distribution

• the assumption of mean = variance for Poisson distribution makes it important to know the dispersion of what you are counting

Negative Binomial Distribution

• observed for count variables when subjects exhibit strongly clumped distributions

Continuous Uniform Distribution

• when all outcomes of the same length are equally probable

• e.g. you show up at a bus stop to wait for a bus that comes by oncer per hour. you do not know what time the bus came by last. The arrival time of the next bus is a continuous uniform distribution [0,1] measured in hours

Normal (Gaussian) Distribution

• the assumed distribution for more parametric statistics covered in this course (bell curve)