Lahiri's method. Lahiri's $(1951)$ method is an example of a rejective method$$you generate a pair of random numbers to select a psu and then to decide whether to accept or reject the psu for the sample. Let N $=$ number of psus in population and max $\{$Mi$\}=$ maximum psu size.

Draw a random number between $1$ and N$.$ This indicates which psu you are considering.

Draw a random number between $1$ and max $\{$Mi$\}.$ If this random number is less than or equal to Mi$,$ then include psu i in the sample; otherwise go back to Step $1.$

Repeat until desired sample size is obtained.