The economy of Nepal is based on the inflow of remittances sent by the Nepalese who have gone abroad for foreign employment. The trend started after the start of the Maoist insurgency and has been going on due to a lack of employment opportunities within the nation. Other than remittance, tourism and a certain amount of foreign aid have been the sources of foreign exchange earnings for Nepal. These sources of FOREX have been able to maintain the balance of payments in Nepal. One unique feature of FOREX rates in Nepal is that the Nepalese rupee (NPR) is pegged with the Indian rupee (INR), the currency of the neighboring nation, India. The central bank of Nepal, Nepal Rastra Bank, publishes FOREX rates for 21 different countries on a daily basis, though exchange rates for 16 currencies have been publishing buying and selling rates for the past decade. Hence, the paper analyzed the distribution nature of 16 countries FOREX buying and selling rates and found that INR FOREX rates have no randomness as they are pegged. The most concerned currencies, like USD, SAR, QAR, and AED, were fitted with beta distribution capabilities to reflect the future trend of the exchange rate. At the same time, the GBP buying rate, JPY, and KRW buying and selling rates were best-fitted in general extreme value (GEV), reflecting the risky nature of currencies. The exchange rate distribution seems to be a concern to the exporter and importer, as the nature of the distribution could help to categorize the level of FOREX risk with a specific currency.