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Binomial distribution

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  Binomial distribution 49 languages Article Talk Read Edit View history From Wikipedia, the free encyclopedia "Binomial model" redirects here. For the binomial model in options pricing, see  Binomial options pricing model . Binomial distribution Probability mass function Cumulative distribution function Notation � ( � , � ) Parameters � ∈ { 0 , 1 , 2 , … }  – number of trials � ∈ [ 0 , 1 ]  – success probability for each trial � = 1 − � Support � ∈ { 0 , 1 , … , � }  – number of successes PMF ( � � ) � � � � − � CDF � � ( � − � , 1 + � )  (the  regularized incomplete beta function ) Mean � � Median ⌊ � � ⌋  or  ⌈ � � ⌉ Mode ⌊ ( � + 1 ) � ⌋  or  ⌈ ( � + 1 ) � ⌉ − 1 Variance � � � Skewness � − � � � � Ex. kurtosis 1 − 6 � � � � � Entropy 1 2 log 2 ⁡ ( 2 � � � � � ) + � ( 1 � ) in  shannons . For  nats , use the natural log in the log. MGF ( � + � � � ) � CF ( � + � � � � ) � PGF � ( � ) = [ � + � � ] � Fisher information � ...