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Template:Infobox probability distribution/testcases

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{{Infobox probability distribution}}{{Infobox probability distribution/sandbox}}
Normal Distribution
Probability density function
Probability density function for the normal distribution
The red curve is the standard normal distribution
Cumulative distribution function
Cumulative distribution function for the normal distribution
Notation
Parameters = mean (location)
= variance (squared scale)
Support
PDF
CDF
Quantile
Mean
Median
Mode
Variance
MAD
Skewness
Excess kurtosis
Entropy
MGF
CF
Fisher information


Kullback–Leibler divergence
Normal Distribution
Probability density function
Probability density function for the normal distribution
The red curve is the standard normal distribution
Cumulative distribution function
Cumulative distribution function for the normal distribution
Notation
Parameters = mean (location)
= variance (squared scale)
Support
PDF
CDF
Quantile
Mean
Median
Mode
Variance
MAD
Skewness
Ex. kurtosis
Entropy
MGF
CF
Fisher information


Kullback-Leibler divergence
Side by side comparison
{{Infobox probability distribution}}{{Infobox probability distribution/sandbox}}
Binomial distribution
Probability mass function
Probability mass function for the binomial distribution
Cumulative distribution function
Cumulative distribution function for the binomial distribution
Notation
Parameters – number of trials
– success probability for each trial
Support – number of successes
PMF
CDF
Mean
Median or
Mode or
Variance
Skewness
Excess kurtosis
Entropy
in shannons. For nats, use the natural log in the log.
MGF
CF
PGF
Fisher information
(for fixed )
Binomial distribution
Probability mass function
Probability mass function for the binomial distribution
Cumulative distribution function
Cumulative distribution function for the binomial distribution
Notation
Parameters – number of trials
– success probability for each trial
Support – number of successes
PMF
CDF
Mean
Median or
Mode or
Variance
Skewness
Ex. kurtosis
Entropy
in shannons. For nats, use the natural log in the log.
MGF
CF
PGF
Fisher information
(for fixed )
Side by side comparison
{{Infobox probability distribution}}{{Infobox probability distribution/sandbox}}
Geometric
Probability mass function
Cumulative distribution function
Parameters success probability (real) success probability (real)
Support k trials where k failures where
PMF
CDF
Mean
Median


(not unique if is an integer)


(not unique if is an integer)
Mode
Variance
Skewness
Excess kurtosis
Entropy
MGF
for
CF
Geometric
Probability mass function
Cumulative distribution function
Parameters success probability (real) success probability (real)
Support k trials where k failures where
PMF
CDF
Mean
Median


(not unique if is an integer)


(not unique if is an integer)
Mode
Variance
Skewness
Ex. kurtosis
Entropy
MGF
for
CF
Side by side comparison
{{Infobox probability distribution}}{{Infobox probability distribution/sandbox}}
Gamma
Probability density function
Probability density plots of gamma distributions
Cumulative distribution function
Cumulative distribution plots of gamma distributions
Parameters
  • α > 0 shape
  • β > 0 rate
  • Support
    PDF
    CDF
    Mean
    Median No simple closed form No simple closed form
    Mode
    Variance
    Skewness
    Excess kurtosis
    Entropy
    MGF
    CF
    Gamma
    Probability density function
    Probability density plots of gamma distributions
    Cumulative distribution function
    Cumulative distribution plots of gamma distributions
    Parameters
  • α > 0 shape
  • β > 0 rate
  • Support
    PDF
    CDF
    Mean
    Median No simple closed form No simple closed form
    Mode
    Variance
    Skewness
    Ex. kurtosis
    Entropy
    MGF
    CF