The purpose of this study is to enable us to obtain mean losses of an insured risk by means of the operational behaviour of density function with deductible modifications and then compare the mean severities under exponentially and log-normally distributed arbitrary policy in a cost per loss and cost per payment circumstances. The mean losses model thus obtained for an arbitrary policy in general insurance under deductible coverage modifications is meant to reduce the number and magnitude of claims received. Furthermore, the mean losses are then used to compute premium numerically, based on the applied deductible. Rate relativity data on deductible was obtained through a non-life insurance agent operating in property insurance market in Lagos. The result show that despite log-normal severity distribution has a thicker tail than the exponential distribution, its cost per loss payment (Y;) is correspondingly lower in value than the values of exponential mean loss that is (YZ )log normal < (YZ)expential. While the cost per payment is uniformly constant throughout the entire domain of definition for the deductible under exponential distribution, the insurer experiences higher cost per payment than expected in the subinterval 45 SD S1 under lognormal regime. It is, therefore, recommended that the insurer is advised to apply deductible in this subdomain to disapprove nuisance claims and control the problem of moral hazard.