If I need to determine the value of a data point at each percentile of a distribution (such as lognormal, weibull, etc), can use its CDF and plug in the percentiles to get the value?

For e.g. finding the value at 95th percentile by plugging in 0.95 in the CDF formula. Basically, I need to determine that if the distribution graph were drawn what data points do I obtain at each percentile. Does CDF tell me the same thing?


The CDF tells you the relationship between a given input $x$ and the probability mass of all inputs $\leq x$. The inverse of the CDF thus tells you the relationship between the probability of mass of all inputs $\leq x$ and x.

For example, consider the distribution $e^{-\lambda x}$. The CDF of this distribution is, by integration, $cdf(x) = 1-e^{-\lambda x}$. If we invert this, we get:

$\frac{log(1-cdf(x))}{-\lambda} = x$

Which tells us that, 95% of the probability mass of the distribution comes before:

$\frac{log(1-0.95)}{-\lambda} = x$


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