vivek - 3 months ago 15
R Question

# Extract approximate probability density function (pdf) in R from random sampling

I have got

`n>2`
independent continuous
`Random Variables(RV)`
. For example say I have
`4 Uniform RVs`
with different set of
`Upper and lowers`
.

``````W~U[-1,5], X~U[0,1], Y~[0,2], Z~[0.5,2]
``````

I am trying to find out the approximate PDF for the sum of these RVs i.e. for
`T=W+X+Y+Z`
. As I don't need any closed form solution, I have sampled
`1 million points`
for each of them to get
`1 million samples for T`
. Is it possible in R to get the approximate PDF function or a way to get approximate probability of
`P(t<T)`
from this samples I have drawn. For example is there a easy way I can calculate
`P(0.5<T)`
in R. My priority here is to get probability first even if getting the density function is not possible.
Thanks

Consider the `ecdf` function:

``````set.seed(123)
W <- runif(1e6, -1, 5)
X <- runif(1e6, 0, 1)
Y <- runif(1e6, 0, 2)
Z <- runif(1e6, 0.5, 2)

T <- Reduce(`+`, list(W, X, Y, Z))
cdfT <- ecdf(T)
1 - cdfT(0.5) # Pr(T > 0.5)
# [1] 0.997589
``````

See How to calculate cumulative distribution in R? for more details.