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Poisson Distribution definitions

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  • Poisson Distribution
    A model for counting occurrences over a fixed interval, relying on a mean rate and suitable for rare events.
  • Binomial Distribution
    A model for counting successes in a fixed number of trials, each with the same probability of success.
  • Occurrence
    An event counted within a fixed interval, such as birds landing or cars passing, central to Poisson modeling.
  • Interval
    A fixed span, often time or space, over which events are counted in Poisson experiments.
  • Mean Rate
    The average number of events expected per interval, represented by lambda in Poisson contexts.
  • Lambda
    A parameter indicating the mean rate of events per interval, used in Poisson probability calculations.
  • Variance
    A measure of spread in Poisson distribution, always equal to the mean rate parameter.
  • Standard Deviation
    A measure of variability in Poisson distribution, calculated as the square root of the mean rate.
  • Probability Distribution Function
    A formula assigning probabilities to each possible count of occurrences in Poisson distribution.
  • Poisson PDF
    A calculator function for finding the probability of exactly a specific number of occurrences.
  • Poisson CDF
    A calculator function for finding the probability of at most a certain number of occurrences.
  • Independence
    A condition where events in different intervals do not affect each other, required for Poisson modeling.
  • Estimation
    The process of using Poisson formulas to approximate binomial probabilities when trials are numerous and success is rare.
  • Factorial
    A mathematical operation used in Poisson probability calculations, multiplying all positive integers up to a given number.
  • Exponential Function
    A mathematical term in Poisson formula, involving e raised to a negative mean rate, crucial for probability computation.