Test whether or not quantile values belong to a distribution I have a list of 23 values for the following quantiles:
[1] 0.010 0.025 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500 0.550 0.600 0.650 0.700 0.750 0.800 0.850
[20] 0.900 0.950 0.975 0.990

I want to test whether or not these quantiles belong to a particular known distribution. My thought was to use calculate a Kolmogorov-Smirnov test statistic, but since I have quantile values and not data I don't know how to find the right p-value.
Any thoughts on how to get an accurate p-value or of another test I can use?

You can plug these probabilities into a friendly  neighbourhood theoretical quantile function and then plot observed quantiles versus expected quantiles.

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*Good news: With those 23 quantiles you have much of the information about the distribution that is available.

*Good news: A graph based on those 23 data points might tell you most of what you need to know. Often it's a matter of informal indication such as "The normal is clearly a poor fit, so what to do next?".

*Bad news: Whatever lies beyond the 1% and 99% points might be extraordinarily important detail, but if you don't have it, you won't know. (Yet how often are the raw data hidden, but only certain quantiles available?)

*Bad news: It will be uphill work turning that into a significance test yielding a P-value, if that is your goal, although many posts here, and many expert opinions elsewhere, imply that you aren't missing much of value.

Kolmogorov-Smirnov is beautiful mathematics, but often oversold statistically.
More crucially, the form of marginal distributions is less important often than variation around systematic structure as approximated by a model.
