It is shown that anomalous X-ray pulsars and soft gamma repeaters are neutron stars with mass less than I solar mass and with magnetic field about 3 x 10(13)-10(14) G. Their ages (t <= 10(5) yr) are considerably larger than their characteristic times. The angle between the rotation axis and the axis of the magnetic field must be large for these objects. From time to time as a result of activities their value of P considerably increases because of the propeller mechanism. Using such an approach Guseinov et al.(1) have predicted the transient characteristic of these sources which has been confirmed recently.(2) We estimate the spatial densities and lifetimes of different types of isolated neutron star. Some of these sources must have relations with anomalous X-ray pulsars and soft gamma repeaters. In order to understand the locations of different types of isolated neutron star on the P-(P)over dot diagram it is also necessary to take into account the differences in the mass and the magnetic field of neutron stars. We have also estimated the birth rates of different types of isolated neutron stars.