I have a data set that has data for the 50th, 60th, 70th, 75th, 80th, 85th, 90th, and 95th percentiles. I am trying to figure out how I should go about calculating the lower percentiles I need (10, 25, 40).
I am using R and am trying to use an estiamted CDF to find these out. Is that the best way to go about this problem?
I am uncertain if it is normally distributed, but I believe it is.
Thank you.
On
Since you don't know the distribution, this is really more of a stats question than a math one so I think fitting a CDF to your data set seems like a sensible approach. If you think it's valid to assume normality, you can use the logistic approximation of the normal CDF to get an estimate of the mean and variance with a curve fitting method of your choice: $\Phi(x|\mu,\sigma^2)\approx\frac{1}{1+\exp\left(\frac{-1.702(x-\mu)}{\sigma}\right)}$. Then simply use a Z-table to get the other percentiles.
If it is normally distributed, then the percentiles lie symmetrically about the mean (the 25th percentile is as far below the mean as the 75th percentile is above the mean, etc.). Lots of other distributions are similarly symmetric. If you do not know the distribution (specifically, if you don't know that it is symmetric), it is impossible to tell where the lower percentiles are from just knowing the your percentiles.