B.2. Distribution Types

Table 3: Discrete Distribution Types

Name	Image	Description
Discrete distribution		Distribution parameter n pairs of: Value x_i Probability Mean value and standard deviation Probability mass function
Bernoulli distribution		Distribution parameter Success probability 0 < p < 1 Mean value and standard deviation Probability mass function
Poisson distribution		Distribution parameter Expected number of events Mean value and standard deviation Probability mass function

Name

Image

Description

Discrete distribution

Distribution parameter

n pairs of:
Value x_i
Probability

Mean value and standard deviation

Probability mass function

Bernoulli distribution

Distribution parameter

Success probability 0 < p < 1

Mean value and standard deviation

Probability mass function

Poisson distribution

Distribution parameter

Expected number of events

Mean value and standard deviation

Probability mass function

Discrete distribution types: distribution parameters, probability mass function , mean value , and standard deviation .

Table 4: Continuous Distribution Types

Name	Image	Description
Uniform distribution		Distribution parameter Lower bound a Upper bound b > a Mean value and standard deviation PDF and CDF
Multi-uniform distribution		Distribution parameter n pairs of: Value Mean value and standard deviation PDF and CDF
Log-uniform distribution		Distribution parameter Lower bound a > 0 Upper bound b > a Mean value and standard deviation PDF and CDF
Normal distribution		Distribution parameter Location parameter μ Scale parameter s > 0 Mean value and standard deviation PDF and CDF
Truncated normal distribution		Distribution parameter Location parameter μ Scale parameter s > 0 Lower bound a Upper bound b Mean value and standard deviation PDF and CDF
Log-normal distribution		Distribution parameter Normal location parameter μ Normal scale parameter s > 0 Mean value and standard deviation PDF and CDF
Triangular distribution		Distribution parameter Lower bound a Mode value c > a Upper bound b > c Mean value and standard deviation PDF and CDF
Exponential distribution		Distribution parameter Scale parameter Shift parameter ϵ Mean value and standard deviation PDF and CDF
Weibull distribution		Distribution parameter Scale parameter λ > 0 Shape parameter k > 0 Mean value and standard deviation PDF and CDF Γ(·) is the gamma function
Frechet distribution		Distribution parameter Scale parameter s > 0 Shape parameter α > 2 Mean value and standard deviation PDF and CDF
Gumbel distribution		Distribution parameter Location parameter μ Scale parameter β > 0 Mean value and standard deviation PDF and CDF γ is the is the Euler-Mascheroni constant
Beta distribution		Distribution parameter Lower bound a Upper bound b Shape parameter α > 0 Shape parameter β > 0 Mean value and standard deviation PDF and CDF B(·,·) is the Beta function B(u, ·,·) is the incomplete Beta function
Lambda distribution		Distribution parameter Location parameter λ₁ Scale parameter λ₂ > 0 Shape parameter λ₃ > -0.25, λ₃ ≠ 0 Shape parameter λ₄ > -0.25, λ₄ ≠ 0 Mean value and standard deviation B(·,·) is the Beta function PDF and inverse CDF CDF is not available in closed form

Continuous distribution types: distribution parameters, probability density function (PDF) , cumulative distribution function (CDF) , mean value , and standard deviation .