VosePoissonLambda

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See also: Cumulative confidence construction estimate for the Poisson intensity

VosePoissonLambda(alpha,t,ProcessExists, U)

Example model

This function generates values for the classical statistics uncertainty distribution for a Poisson intensity (lambda) estimated from data, using the technique explained here.

• Alpha - the number of Poisson observations made in time t. This must be a positive integer.

• t - the time over which Alpha observations were made.

• ProcessExists - Optional boolean parameter (TRUE/FALSE). TRUE (or omitted) for when it is known that the possibility of observations >0. FALSE applies when alpha = 0 to allow possibility that observations cannot be observed (Lambda = 0)

• U - (optional) The cumulative confidence associated with the estimate of lambda. If omitted the function generates random values.

This function has, like all the distributions in ModelRisk, an optional U-parameter.

Example 1

An insurance company X is about to insure a big chemical company who in the past have had to deal with clients suing them and where a few times this chemical company lost the case against the client. In the last three years (t = 3) this has not happened anymore though, which means that there were no observations (alpha = 0) but we know that it could happen (ProcessExists = 1). A way to model the uncertainty for the Poisson intensity of losing a court case is to use the formula:

=VosePoissonLambda(0,3,1)

If the chemical company had been sued 3 times in the last seven years, for example, we would estimate lambda as:

=VosePoissonLambda(3,7,1)

or

=VosePoissonLambda(3,7,0)

The last parameter ProcessExists becomes redundant in this case since the data (alpha > 0) demonstrate that the risk does indeed exist.

Example 2

Now, imagine a similar case where an insurance company Y insures a pharmaceutical company. The insurance company knows about the possible court cases insurance company X had to face in the past but they don't know if the same thing could happen with the pharmaceutical company they are insuring (this means that ProcessExists = 0 in this case).

Suppose that they haven't seen it happen in the 7 years that this pharmaceutical company exists (alpha = 0, t = 7).

Now to model the uncertainty for the Poisson intensity lambda of losing a court case we can use the formula:

 =VosePoissonLambda(0,7,0)