MinimumQuantileInformation {mc2d} | R Documentation |
Minimum Quantile Information Distribution
Description
Density, distribution function, quantile function and random generation for Minimum Quantile Information distribution.
Usage
dmqi(x,
mqi,
mqi.quantile = c(0.05, 0.5, 0.95),
realization = NULL,
k = 0.1,
intrinsic = NA,
log = FALSE)
pmqi(q,
mqi,
mqi.quantile = c(0.05, 0.5, 0.95),
realization = NULL,
k = 0.1,
intrinsic = NA,
lower.tail = TRUE,
log.p = FALSE
)
qmqi(p,
mqi,
mqi.quantile = c(0.05, 0.5, 0.95),
realization = NULL,
k = 0.1,
intrinsic = NA,
lower.tail = TRUE,
log.p = FALSE
)
rmqi(n,
mqi,
mqi.quantile = c(0.05, 0.5, 0.95),
realization = NULL,
k=0.1,
intrinsic = NA
)
pmqi(
q,
mqi,
mqi.quantile = c(0.05, 0.5, 0.95),
realization = NULL,
k = 0.1,
intrinsic = NA,
lower.tail = TRUE,
log.p = FALSE
)
qmqi(
p,
mqi,
mqi.quantile = c(0.05, 0.5, 0.95),
realization = NULL,
k = 0.1,
intrinsic = NA,
lower.tail = TRUE,
log.p = FALSE
)
rmqi(
n,
mqi,
mqi.quantile = c(0.05, 0.5, 0.95),
realization = NULL,
k = 0.1,
intrinsic = NA
)
Arguments
x , q |
Vector of quantiles |
mqi |
Minimum quantile information |
mqi.quantile |
The quantile of ‘mqi'. It’s a vector of length 3. Default is 'c(0.05, 0.5, 0.95)', that is the 5th, 50th and 95th. |
realization |
Default is 'NULL'. If not 'NULL', used to define 'L' or 'U' (see details). |
k |
Overshot, default value is 0.1. |
intrinsic |
Use to specify a prior bounds of the intrinsic range. Default = 'NA'. |
log , log.p |
Logical; if 'TRUE', probabilities 'p' are given as 'log(p)'. |
lower.tail |
Logical; if 'TRUE' (default), probabilities are 'P[X <= x]' otherwise, 'P[X > x]'. |
p |
Vector of probabilities. |
n |
Number of observations. |
Details
,
, and
are percentiles of a distribution with
.
The interval
is given with:
The support of minimum quantile information distribution is determined by the intrinsic range:
where denotes an overshoot and is chosen by the analyst (usually
, which is the default value).
Given the three values of quantile, ,
and
,
and define
,
,
and
the minimum quantile information distribution is given by:
Probability density function
Cumulative distribution function
This distribution is usually used for expert elicitation.
If experts have realization information, then the range is given by:
For some questions, experts may have information for the intrinsic range and set a prior intrinsic range ( and
).
NOTE that the function is vectorized only for x, q, p, n. As a consequence, it can't be used for variable other parameters.
Author(s)
Yu Chen and Arie Havelaar
References
Hanea, A. M., & Nane, G. F. (2021). An in-depth perspective on the classical model. In International Series in Operations Research & Management Science (pp. 225–256). Springer International Publishing.
Examples
curve(dmqi(x, mqi=c(40,50,60), intrinsic=c(0,100)), from=0, to=100, type = "l", xlab="x",ylab="pdf")
curve(pmqi(x, mqi=c(40,50,60), intrinsic=c(0,100)), from=0, to=100, type = "l", xlab="x",ylab="cdf")
rmqi(n = 10, mqi=c(555, 575, 586))