Modelling of data of claim amount is of paramount importance to manage risk reserve for payment of claims. Actuaries model uncertainty using probability distributions. In this research paper claim amount distribution of the data of an insurance concern has been estimated and analysis was performed on big-data of claim amounts for better understanding and fitting of various probability distribution using R. It was noticed that the claim amounts distribution is highly positive skewed, therefore we have studied Exponential distribution, Gamma distribution and Weibull distribution as possible candidates for modelling the claim amount data. Chi Square test has been used as goodness of fit technique to decide suitable statistical model to representing the claim amounts under study. Exponential distribution is found suitable for modelling the data under study. Proposed model is usefulto estimate claim amount on aggregate for insurance concern when total loss is required to be computed to manage the risk reserve for the payments of claims.