Enterprise Risk Management Formula Book

1. Function Definitions

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1.1          Gamma function,



Defined for ,  not a negative integer. Other properties: . If  is a positive integer then . .


1.2          Incomplete gamma function, , beta function, , incomplete beta function, , regularised incomplete beta function,



The beta function is related to the gamma function as follows:



The gamma, incomplete gamma, beta, incomplete beta and regularised incomplete beta can also be defined for negative (non-integral) values of  and  and for complex (non-real) values by analytic continuation.


1.3          The binomial coefficient,


For  and  integers  this is defined as:



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