Three approaches to a nonparametric maximum likelihood problem are considered. One, based on the method of "sieves", is shown to include the other two. The sieve considered is a double exponential convolution sieve. A closed form solution is given for certain values of the sieve parameter.
"A Simple Solution to a Nonparametric Maximum Likelihood Estimation Problem." Ann. Statist. 12 (1) 372 - 379, March, 1984. https://doi.org/10.1214/aos/1176346415