#StackBounty: #probability #distributions #pdf #quantiles #cdf Find the PDF from quantiles

Bounty: 50

I have been presented a problem of this kind:
suppose I know the values of k quantiles for a continuous random variable $X$

$$X_{1%} = x_1, X_{5%} = x_2, dots , X_{99%} = x_{k}$$

so that

$$ F_X(x_1)=1%, F_X(x_2)=5%, dots, F_X(x_k)=99% $$

From these informations I want to draw the chart of the PDF.

I thought that I could proceed this way:

  • interpolate $F_X(x)$ to get a smooth CDF (for instance spline interpolation)
  • find the derivative (numerical) of the smoothed CDF at some points to obtain the PDF.

Are there other more direct methods to address this problem? Do you think my solution is solid?

Thank you.

Get this bounty!!!

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