Theinverse transform sampling method is a method of sampling a number atrandom from anyprobability distribution, given itscumulative distribution function (cdf).

The problem that the inverse transform sampling method solves is as follows:

• Anggap X bakal jadivariabel acak nu mana sebaranna bisa dijelaskeun ku cdf d(x).
• We want to generate values ofx which are distributed according to this distribution.

Manyprogramming languages have the ability to generatepseudo-randomnumbers which are effectively distributed according to the standardsebaran seragam. If a random variable has that distribution, then the probability of its falling within any subinterval (a,b) of the interval from 0 to 1 is just the lengthb -a of that subinterval.

The inverse transform sampling method works as follows:

1. Generate a random number from the standard uniform distribution; call thisu.
2. Compute the value forx which has the associated cdf valueu; call thisx_chosen.
3. Takex_chosen to be the random number drawn from the distribution described by d(x).

The following diagram may help the réader to visualise how the method works:

Therejection sampling method.

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