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One of the fundamental features of space plasmas is the observation of non-Maxwellian particle velocity distributions. In the present study, we observe electron velocity distributions in the Earth's magnetosphere at times when the electron density is low, typical of cusp values, and when it is enhanced as a result of disturbances by the solar wind. We find that electron distributions are flat-topped and have two populations: one cold and one hot. We fit the observed electron distributions by a generalized $( {r,q} )$ distribution, and derive and plot expressions for the real frequency and growth rate using fitted and observed parameters. We show that enhancement in the density of hot electrons enhances the growth rate of whistler waves, which play an important role in energy transport in the Earth's magnetosphere.