A dispersion relation for the instability of the coupled drift compressional drift mirror, and shear Alv¿n waves in the magnetospheric plasma is analyzed by numerical method. The analysis is suitable for the storm time plasma conditions in the magnetosphere which usually has gradients in plasma density temperature, magnetic field, and anisotropy in temperature. The effect of high &bgr; which is characteristic of storm time plasma is included in the model. For a given appropriate set of plasma parameters, and wave parameters of a mode relative wave amplitudes are calculated from the model. A comparison is made of model generated and observed relative wave amplitudes by using two sample wave events observed by Explorer 45 during the August 4--6, 1972, magnetic storm. The quantitative analysis shows good agreement between theory and observations for a gradient-driven Alv¿nlike instability; however, growth rates are veery small for this mode. The anisotropy-driven drift mirror instability has large growth rates but does not show correlation between theory and observations of relative wave amplitudes.