This seems to be a pretty basic question for this forum, please bear with me.Consider that I have 10,000 measurements, say of the height of 10,000 people. These height measurements vary from 140 to 190 cm. I now define three height-groups: short (&lt;150 cm), medium (150 to 170 cm) and tall (&gt;170 cm). I can now calculate proportions of those groups in my set of 10,000 people (eg: “40% of the people are short, 30% are medium, 30% are tall”).Now, consider that there is a random error associated with each of the height measurements. By a separate experiment, I concluded that this error distribution is well-approximated by a normal distribution, with a mean of zero and a standard deviation of 10 cm. That is, the measurers are unbiased, but do make some random errors.Now, I would like to propagate this estimated error in height measurement to the proportions. That is, I would like to say something like “the percent of short men in 40 ± 3 %” ( ± could be standard error). Is there a theoretical way to go about this problem, rather than resorting to a Monte Carlo simulation?The original data of 10,000 measurements could be described in two ways:1. It is approximated by another normal distribution, of mean 165 cm and a standard deviation of 7.0 cm2. It is described in a programming language data structure context; it is in a R vector, say "origData". Here, I am expecting R code that will take this vector and other inputs (from the question) and give me the standard errors.

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This seems to be a pretty basic question for this forum, please bear with me.Consider that I have 10,000 measurements, say of the height of 10,000 people. These height measurements vary from 140 to 190 cm. I now define three height-groups: short (&amp;lt;150 cm), medium (150 to 170 cm) and tall (&amp;gt;170 cm). I can now calculate proportions of those groups in my set of 10,000 people (eg: “40% of the people are short, 30% are medium, 30% are tall”).Now, consider that there is a random error associated with each of the height measurements. By a separate experiment, I concluded that this error distribution is well-approximated by a normal distribution, with a mean of zero and a standard deviation of 10 cm. That is, the measurers are unbiased, but do make some random errors.Now, I would like to propagate this estimated error in height measurement to the proportions. That is, I would like to say something like “the percent of short men in   40  ±  3  %” (  ± could be standard error). Is there a theoretical way to go about this problem, rather than resorting to a Monte Carlo simulation?The original data of 10,000 measurements could be described in two ways:1. It is approximated by another normal distribution, of mean 165 cm and a standard deviation of 7.0 cm2. It is described in a programming language data structure context; it is in a R vector, say &quot;origData&quot;. Here, I am expecting R code that will take this vector and other inputs (from the question) and give me the standard errors.

iskakanjulc · Accepted Answer

For a continuous distribution of values, you can apply a Weierstrass Transform. This basically takes the value at every point and spreads it out according to the normal distribution. The Weierstrass Transform is a type of convolution.For discrete distributions, you can use a Gaussian Blur, which is the discrete version of a Weierstrass Transform.Either way, you end up with a new distribution. You can then compare this new distribution with your original distribution and calculate errors from there.

This seems to be a pretty basic question for this forum, please bear with me. Consider that I have

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