CODEWITHSUNDEEP
rprobability-density
Hercules Apergis
Hercules Apergis

Reputation: 421

Probability Density (pdf) extraction in R

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I am attempting to reproduce the above function in R. The numerator has the product of the probability density function (pdf) of "y" at time "t". The omega_t is simply the weight (which for now lets ignore). The i stands for each forecast of y (along with the density) derived for model_i, at time t.

The denominator is the integral of the above product. My question is: How to estimate the densities. To get the density of the variable one needs some datapoints. So far I have this:

y<-c(-0.00604,-0.00180,0.00292,-0.0148)
forecastsy_model1<-c(-0.0183,0.00685) # respectively time t=1 and t=2 of the forecasts
forecastsy_model2<-c(-0.0163,0.00931) # similarly
all.y.1<-c(y,forecasty_model1) #together in one vector 
all.y.2<-c(y,forecasty_model2) #same

However, I am not aware how to extract the density of x1 for time t=1, or t=6, in order to do the products. I have considered this to find the density estimated using this:

dy1<-density(all.y.1)
which(dy1$x==0.00685)
integer(0) #length(dy1$x) : 512

with dy1$x containing the n coordinates of the points where the density is estimated, according to the documentation. Shouldn't n be 6, or at least contain the points of y that I have supplied? What is the correct way to extract the density (pdf) of y?

Upvotes: 1

Views: 705

Answers (1)

Zheyuan Li
Zheyuan Li

Reputation: 73315

There is an n argument in density which defaults to 512. density returns you estimated density values on a relatively dense grid so that you can plot the density curve. The grid points are determined by the range of your data (plus some extension) and the n value. They produce a evenly spaced grid. The sampling locations may not lie exactly on this grid.

You can use linear interpolation to get density value anywhere covered by this grid:

Upvotes: 2

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