Approximating discrete distribution by continuous distribution
On 22/01/2013 11:49, Michael Haenlein wrote:
Dear all,
I have a discrete distribution showing how age is distributed across a
population using a certain set of bands:
Age <- matrix(c(74045062, 71978405, 122718362, 40489415), ncol=1,
dimnames=list(c("<18", "18-34", "35-64", "65+"),c()))
Age_dist <- Age/sum(Age)
For example I know that 23.94% of all people are between 0-18 years, 23.28%
between 18-34 years and so forth.
I would like to find a continuous approximation of this discrete
distribution in order to estimate the probability that a person is for
example 16 years old.
Is there some automatic way in R through which this can be done? I tried a
Kernel density estimation of the histogram but this does not seem to
provide what I'm looking for.
This is not really an R question, but a statistics one. It is almost guesswork: if for example these were drivers in the UK, the answer is 0. So you need to supply some information about the shape of the distribution of <18 year olds. You have estimates of the cumulative distribution function at c(0, 18, 35, 65, Inf) (or some better upper limit). You want to interpolate it. You could use linear interpolation (approx[fun]) or a monotone spline interpolation (spline[fun]) or any other interpolation method which meets your needs. But whatever you use, you will supplying a lot of information not actually in your data.
Thanks very much for your help, Michael Michael Haenlein Associate Professor of Marketing ESCP Europe Paris, France [[alternative HTML version deleted]]
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