ProbabilityDistributionType |
Lvl |
Type, Domain name and/or Mnemonic code |
Concept ID |
Mnemonic |
Print Name |
Definition/Description |
1
|
L: (B)
|
10756 |
B |
beta |
The beta-distribution is used for data that is bounded on both sides and may or may not be skewed (e.g., occurs when probabilities
are estimated.) Two parameters ? and ? are available to adjust the curve. The mean ? and variance ?2 relate as follows:
?
|
1
|
L: (E)
|
10752 |
E |
exponential |
Used for data that describes extinction. The exponential distribution is a special form of ?-distribution where ? = 1, hence,
the relationship to mean ? and variance ?2 are ? = ? and ?2 = ?2.
|
1
|
L: (F)
|
10755 |
F |
F |
Used to describe the quotient of two ?2 random variables. The F-distribution has two parameters ?1 and ?2, which are the
numbers of degrees of freedom of the numerator and denominator variable respectively. The relationship to mean ? and variance
?2 are
|
1
|
L: (G)
|
10751 |
G |
(gamma) |
The gamma-distribution used for data that is skewed and bounded to the right, i.e. where the maximum of the distribution curve
is located near the origin. The ?-distribution has a two parameters ? and ?. The relationship to mean ? and variance ?2
is ? =
|
1
|
L: (LN)
|
10750 |
LN |
log-normal |
The logarithmic normal distribution is used to transform skewed random variable X into a normally distributed random variable
U = log X. The log-normal distribution can be specified with the properties mean ? and standard deviation ?. Note however
that m
|
1
|
L: (N)
|
10749 |
N |
normal (Gaussian) |
This is the well-known bell-shaped normal distribution. Because of the central limit theorem, the normal distribution is
the distribution of choice for an unbounded random variable that is an outcome of a combination of many stochastic processes.
Even f
|
1
|
L: (T)
|
10754 |
T |
T |
Used to describe the quotient of a normal random variable and the square root of a ?2 random variable. The t-distribution
has one parameter ?, the number of degrees of freedom. The relationship to mean ? and variance ?2 are: ? = 0 and ?2 = ? /
(? ? 2)
|
1
|
L: (U)
|
10748 |
U |
uniform |
The uniform distribution assigns a constant probability over the entire interval of possible outcomes, while all outcomes
outside this interval are assumed to have zero probability. The width of this interval is 2 ? ?3. Thus, the uniform distribution
as
|
1
|
L: (X2)
|
10753 |
X2 |
chi square |
Used to describe the sum of squares of random variables which occurs when a variance is estimated (rather than presumed) from
the sample. The only parameter of the ?2-distribution is ?, so called the number of degrees of freedom (which is the number
of i
|