
Dear R users,

I am working on the Value at Risk (VaR) for the Operational risk. For a given loss data, we try to fit some statistical distributions using Kolmogorov-Smirnov (KS) test and A-D test and then for fitted distribution using the estimated parameters, the losses are simulated and the VaR is arrived at. 

The typical problem faced by the banks is the paucity of Internal loss data and thus banks depend on the external loss data obtained from external sources. This external data is normally of higher magnitude than the internal loss data of the bank. Thus using regression technique, this external data is scaled and then the internal data and the scaled external data is combined. Then we try to fit some statistical distribution to this combined data. However, at times it becomes very difficult to fit any distribution to this particular combined data as the data becomes Bimodal.

The paper by G. Dionne and Hela Dahen " What about underevaluating Operational Value at Risk in the Banking sector?" suggests that we fit two distributions 

(1) to the internal data (called body part) with Upper cap or upper bound to the loss data and 

(2) to the external data with Lower bound (called Tail part). 

Thus, now I am dealing with two truncated distributions (i) having a lower loss bound (say 5000$ i.e. bank records only those losses exceeding 5,000$) and having an Upper bound of say 500,000$; and (ii) having lower loss bound of say 500,000$ and no upper limit.

My question is 

(1) Is there any R package which helps to estimate the parameters of "various" Truncated distributions?

(2) How to fit the truncated distributions to loss data in the sense how do we use KS and AD tests?

Extremely sorry for writing such a long mail.

Regards

Julia


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