1.3.6.6.19. Poisson Distribution | poisson distribution lambda
1.ExploratoryDataAnalysis[1]1.3.EDATechniques[2]1.3.6.ProbabilityDistributions[3]1.3.6.6.GalleryofDistributions[4]1.3.6.6.19.PoissonDistributionProbabilityMassFunction[5]ThePoissondistributionisusedtomodelthenumberofeventsoccurringwithinagiventimeinterval.TheformulaforthePoissonprobabilitymassfunctionis(p(x;lambda)=frac{e{-lambda}lambda{x}}{x!}mbox{for}x=0,1,2,cdots)λistheshapeparameterwhichindicatestheaveragenumberofeventsinthegiventimeinterval.ThefollowingistheplotofthePoissonprobabilityde...
1. Exploratory Data Analysis[1] 1.3. EDA Techniques[2] 1.3.6. Probability Distributions[3] 1.3.6.6. Gallery of Distributions[4] 1.3.6.6.19. Poisson Distribution Probability Mass Function [5] The Poisson distribution is used to model the number of events occurring within a given time interval.The formula for the Poisson probability mass function is
( p(x;lambda) = frac{e{-lambda}lambda{x}} {x!} mbox{ for } x = 0, 1, 2, cdots )
λ is the shape parameter which indicates the average number of events in the given time interval.
The following is the plot of the Poisson probability density function for four values of λ.
Cumulative Distribution Function [6] The formula for the Poisson cumulative probability function is
( F(x;lambda) = sum_{i=0}{x}{frac{e{-lambda}lambda{i}} {i!}} )
The following is the plot of the Poisson cumulative distribution function with the same values of λ as the pdf plo...