Distribution generator

Uniform Normal Binomial Poisson Χ2 Chi-squared Lognormal
Start:
End:-1
Mean μ x̄:
Std dev. σ s:
n:
p:
λ: k: μ:
σ:

Discrete     Continuous


How many?


Uniform distribution: every datum in range equally likely.
mean=(start+end)/2 ie. midrange
standard deviation= (end-start)/√12 ≈ (end-start)/3.464
skew: 0

Normal/Gaussian distribution: physical quantity that is the sum of many small independent processes. Also, distribution of sample averages.
mean=median=mode
skew: 0
kurtosis: 0

Binomial distribution: #successes/yeses/ones in n tries when probability of a success is p.
mean= np
standard deviation= √(np(1-p))
skew: (1-2p)/σ
kurtosis: (1-6p(1-p))/σ2
n=1 : Bernoulli distribution. p=proportion success

Poisson distribution: λ=expected/average independent #events in an interval. Probabilities of each k (0-) #occurences/events/arrivals in an interval.
mean= λ
standard deviation= √λ
skew: 1/√λ
kurtosis: 1/√λ

Χ2 Chi-squared distribution: sum of k squared standard normals
mean= k
standard deviation= √(2k)
skew:√(8/k)
kurtosis: 12/k ?

Lognormal distribution: its log is normally distributed. μ and σ are mean and standard deviation of that normal distribution.
mean= eμ+σ2/2
mode= eμ-σ2
median= eμ
mode<median<mean
standard deviation= eμ+σ2/2√(eσ2-1)