Two methods to determine the electromagnetic wave distribution function are presented. The first is based on the use of the dirichlet kernels and provides us with a local average. It has the disadvantage, however, of a nonsystematic approach to positive solutions. The second uses the maximum entropy concept. It leads to particular solutions that are smooth and positive everywhere. The two methods are shown to be complementary. Applications to VLF electromagnetic waves observed onboard Geos 1 are discussed. One of the most striking results is that the wave energy of the natural VLF emissions is generally concentrated within two wave packets whose wave normals are approximately in the same off-meridian plane and oriented in the same way relative to the direction of the earth's magnetic field. It is suggested that those two wave packets have a common source.