# [R] random draw from a RESTRICTED pareto distribution

Kairos2012 lucie.salwiczek at zooplus.de
Mon Jan 21 12:51:40 CET 2013

```Dear R user,

I am a newcomer and need help concerning 'draw a random number for a
restricted area of a prareto distribution'.

(1) For estimation of pareto distribution:
>http://stats.stackexchange.com/questions/27426/how-do-i-fit-a-set-of-data-to-a-pareto-distribution-in-r<

We calculate the pareto distribution (parameter estimation) as follows:

pareto.MLE  <- function(X)
{
n         <- length(X)
m         <- min(X)
a         <- n/sum(log(X)-log(m))
return( c(m,a) )
}
par.eto.par <- c(s=pareto.MLE(data\$T), beta=pareto.MLE(data\$T))

[NOTE: data\$T: the data we use]

(2) Current random draw from an unrestricted pareto distribution:
library(VGAM)
random  <- rpareto(l, location=beta, shape=s)

[Note: s and beta are calculated in (1)]

(3) What we need instead of step (2) is a random draw from an RESTRICTED
pareto distribution, using the pareto parameters calculated (1), where
random ≥ data\$T

This means:
- Then make a random draw from a pareto distribution using the parameters
(s, beta) estimated in (1)
- and this new = randomly drawn number (‘random’) should be ≥ a given value
from data\$T.

Problem:
If the area from which to draw a new number is not restricted, this new
number (‘random’) can be smaller than the value from data\$T.

- if random < data\$T then run as many random draws as it needs until the new
number (‘random’)  fulfills the requirement random ≥ ta.data\$T.
Of course, that is not efficient, it takes a lot of time.

Alternative: restrict the area from which to draw the random numbers.
BUT: I don’ know how to restrict the area where the random draw occurs.*

Thus the question is: how to tell R to use for the random draw only the area
from a given pareto distribution with parameters estimated in (1) where
random ≥ ta.data\$T ?

Thanks for any thoughts and advice on this!

--
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