Download Parameters

Commonly used distributions
Normal distribution
( )
Formula:
(
)
√
Domain:
Parameters:
Mean
standard deviation
Uniform distribution (real number form)
( )
Formula:
{
Domain:
Parameters:
Low X, High X
Uniform distribution (integer number form)
( )
Formula:
{
Domain:
Parameters:
Triangular distribution
Formula:
( )
{
(
)
(
) (
Domain:
Parameters:
Low X, Mode (likeliest), High X
)
Fractile distributions (10/50/90 et al)
Formula:
Equal probability for Low X and High X (e.g., .30 or .25,
remainder for Median, 0 for other values.
Domain:
Low X, Median X, High X
Parameters:
Low X, Median X, High X
More continuous distributions
Beta distribution (integer form)
Formula:
(
( )
(
)
)(
(
)
)
Domain:
Parameters:
Details:
Beta distribution (real number form)
Formula:
(
( )
)(
)(
)
(
)
( ) ( )
Domain:
Parameters:
Details:
(
)
The parameters a and b can be approximated from a mean μ
and standard deviation σ:
(
(
(
)
)( (
)
)
)
Dirichlet distribution (multivariate, normalized beta)
Formula:
where
∑
where ∑
Domain:
Parameters:
Details:
See Chapter 22.
Chi distribution
Formula:
( )
( )
(
( )
Domain:
Parameters:
Chi-Squared distribution
Formula:
Domain:
Parameters:
( )
(
(
)
)
( )
)
Erlang distribution
Formula:
( )
(
)
(
)
Domain:
Parameters:
Exponential distribution
Formula:
( )
Domain:
Parameters:
Gamma distribution
Formula:
( )
(
)
( )
Domain:
Parameters:
Details:
The parameters and can be approximated from a mean μ
and standard deviation σ:
Hyper-exponential distribution
Formula:
( )
(
Domain:
Parameters:
Laplace distribution
Formula:
|
( )
|
Domain:
Parameters:
Logistic distribution
Formula:
Domain:
Parameters:
( )
(
(
)
(
))
)
(
)
Lognormal distribution
Formula:
(
( )
(
( )
)
)
√
Domain:
Parameters:
Details:
The parameters and are the mean and standard deviation
respectively, from the distribution of the ln(x), and can be
approximated:
(
√
)
(
)
Maxwell distribution
Formula:
( )
√
Domain:
Parameters:
Rayleigh distribution
Formula:
Domain:
Parameters:
( )
(
)
Weibull distribution
Formula:
( )
Domain:
Parameters:
More discrete distributions
Binomial distribution
Formula:
( )
( )
(
)
Domain:
Parameters:
Poisson distribution
Formula:
Domain:
Parameters:
(
)