View source: R/distributions.R
tfd_pert | R Documentation |
The PERT distribution is a loc-scale family of Beta distributions
fit onto a real interval between low
and high
values set by the user,
along with a peak
to indicate the expert's most frequent prediction,
and temperature
to control how sharp the peak is.
tfd_pert( low, peak, high, temperature = 4, validate_args = FALSE, allow_nan_stats = FALSE, name = "Pert" )
low |
lower bound |
peak |
most frequent value |
high |
upper bound |
temperature |
controls the shape of the distribution |
validate_args |
Logical, default FALSE. When TRUE distribution parameters are checked for validity despite possibly degrading runtime performance. When FALSE invalid inputs may silently render incorrect outputs. Default value: FALSE. |
allow_nan_stats |
Logical, default TRUE. When TRUE, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When FALSE, an exception is raised if one or more of the statistic's batch members are undefined. |
name |
name prefixed to Ops created by this class. |
The distribution is similar to a Triangular distribution
(i.e. tfd.Triangular
) but with a smooth peak.
Mathematical Details
In terms of a Beta distribution, PERT can be expressed as
PERT ~ loc + scale * Beta(concentration1, concentration0)
where
loc = low scale = high - low concentration1 = 1 + temperature * (peak - low)/(high - low) concentration0 = 1 + temperature * (high - peak)/(high - low) temperature > 0
The support is [low, high]
. The peak
must fit in that interval:
low < peak < high
. The temperature
is a positive parameter that
controls the shape of the distribution. Higher values yield a sharper peak.
The standard PERT distribution is obtained when temperature = 4
.
a distribution instance.
For usage examples see e.g. tfd_sample()
, tfd_log_prob()
, tfd_mean()
.
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