Calculate mean of a CDF

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Nathalie
Nathalie il 1 Mag 2014
Risposto: Prateekshya il 21 Ott 2024
Can you please help to calculate mean on some interval [a,b]: $\underset{a}{\overset{b}{\int}}\theta dF\left(\theta\right)$ knowing F(theta). Thanks in advance

Risposte (1)

Prateekshya
Prateekshya il 21 Ott 2024
Hello Nathalie,
To calculate the mean of a function θ over an interval with respect to a cumulative distribution function (CDF) , you need to evaluate the integral:
This is essentially the expectation of over the interval . If is a CDF, then its derivative, , is the probability density function (PDF). The integral can be rewritten using this PDF:
Steps to Calculate the Mean:
  • Identify the PDF: Differentiate the CDF to obtain the PDF .
  • Set Up the Integral: Use the PDF to set up the integral for the mean:
  • Evaluate the Integral: Compute the integral using analytical or numerical methods.
I hope this helps!

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