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The number of sudden spin-ups in radio pulsars known as pulsar glitches hasincreased over the years. Though a consensus has not been reached with regardsto the actual cause of the phenomenon, the electromagnetic braking torque onthe crust quantified via the magnitude of pulsar spin frequency firstderivative, $ \dot{\nu} $ is a key factor in mechanisms put across toward theunderstanding of the underlying principles involved. The glitch size has beenused to establish a quantity used to constrain the mean possible change inpulsar spin frequency $ (\nu) $ per year due to a glitch known as the `glitchactivity'. Traditionally, the glitch activity parameter $ A_{g} $ is calculatedfrom the cumulative glitch sizes in a pulsar at a certain observational timespan. In this analysis, we test the possibility of of quantifying the $ A_{g} $with the pulsars main spin frequency derivatives (i.e. $ \dot{\nu} $ and$\ddot{\nu} $). In this approach, the ratio of the frequency derivatives, i.e.$ |\ddot{\nu}|/\dot{\nu}^{2} $ is seen to constrains the glitch activity inradio pulsars. The glitch size is found to be independent of the magnitude ofthe ratio, however, based on the recorded glitch events, the lower end of $|\ddot{\nu}|/\dot{\nu}^{2} $ distribution appear to have more glitches. Theminimum inter-glitch time interval in the ensemble of pulsars scale with theratio as $t_{g} \sim 3.35(|\ddot{\nu}|/\dot{\nu}^{2})^{0.23} $. The $ A_{g} $quantified in this analysis supports the idea of neutron star inner-crustsuperfluid being the reservoir of momentum transferred during glitches. Itsuggests that the moment of inertia of the inner-crust to be at most 10 % ofthe entire neutron star moment of inertia.

On the pulsar spin frequency derivatives and the glitch activity