betaPERT {prevalence} | R Documentation |
The Beta-PERT methodology allows to parametrize a generalized Beta distribution based on expert opinion regarding
a pessimistic estimate (minimum value), a most likely estimate (mode),
and an optimistic estimate (maximum value). The betaPERT
function incorporates two methods of
calculating the parameters of a Beta-PERT distribution, designated "classic"
and "vose"
.
betaPERT(a, m, b, k = 4, method = c("classic", "vose"))
## S3 method for class 'betaPERT'
print(x, conf.level = .95, ...)
## S3 method for class 'betaPERT'
plot(x, y, ...)
a |
Pessimistic estimate (Minimum value) |
m |
Most likely estimate (Mode) |
b |
Optimistic estimate (Maximum value) |
k |
Scale parameter |
method |
|
x |
Object of class |
y |
Currently ignored |
conf.level |
Confidence level used in printing quantiles of resulting Beta-PERT distribution |
... |
Other arguments to pass to function |
The Beta-PERT methodology was developed in the context of Program Evaluation and Review Technique (PERT). Based on a pessimistic estimate (minimum value), a most likely estimate (mode), and an optimistic estimate (maximum value), typically derived through expert elicitation, the parameters of a Beta distribution can be calculated. The Beta-PERT distribution is used in stochastic modeling and risk assessment studies to reflect uncertainty regarding specific parameters.
Different methods exist in literature for defining the parameters of a Beta distribution based on PERT. The two most common methods are included in the BetaPERT
function:
The standard formulas for mean, standard deviation, \alpha
and \beta
, are as follows:
mean = \frac{a + k*m + b}{k + 2}
sd = \frac{b - a}{k + 2}
\alpha = \frac{mean - a}{b - a} * \left\{ (mean - a) * \frac{b - mean}{sd^{2}} - 1 \right\}
\beta = \alpha * \frac{b - mean}{mean - a}
The resulting distribution is a 4-parameter Beta distribution: Beta(\alpha
, \beta
, a, b).
Vose (2000) describes a different formula for \alpha
:
(mean - a) * \frac{2 * m - a - b}{(m - mean) * (b - a)}
Mean and \beta
are calculated using the standard formulas; as for the classical PERT,
the resulting distribution is a 4-parameter Beta distribution: Beta(\alpha
, \beta
, a, b).
Note: If m = mean
, \alpha
is calculated as 1 + k/2
, in accordance with the mc2d package (see 'Note').
A list of class "betaPERT"
:
alpha |
Parameter |
beta |
Parameter |
a |
Pessimistic estimate (Minimum value) |
m |
Most likely estimate (Mode) |
b |
Optimistic estimate (Maximum value) |
method |
Applied method |
Available generic functions for class "betaPERT"
are print
and plot
.
The mc2d package provides
the probability density function, cumulative distribution function, quantile function and random number generation function
for the PERT distribution, parametrized by the "vose"
method.
Brecht Devleesschauwer <brechtdv@gmail.com>
Malcolm DG, Roseboom JH, Clark CE, Fazar W (1959) Application of a technique for research and development program evaluation. Oper Res 7(5):646-669.
David Vose. Risk analysis, a quantitative guide, 2nd edition. Wiley and Sons, 2000.
PERT distribution in ModelRisk (Vose software)
betaExpert
, for modelling a standard Beta distribution based on expert opinion
## The value of a parameter of interest is believed to lie between 0 and 50
## The most likely value is believed to be 10
# Classical PERT
betaPERT(a = 0, m = 10, b = 50, method = "classic")
# Vose parametrization
betaPERT(a = 0, m = 10, b = 50, method = "vose")