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This Windows DLL contains a collection of value functions based on exponential utility that are used in Decision Analysis to place a dollar value on an uncertain monetary outcome. The concept behind these function is the "certainty equivalent" idea, which asserts that there is a cash equivalent for any monetary gamble, which is that sum of money which the decision maker would feel indifference in relation to the given monetary gamble. The arguments of the function include the risk tolerance of the decision maker and the parameters of the distribution. For example, in the case of a normal distribution with mean m and standard deviation s, the function call would be =CE_NORMAL(t, m, s) and the value returned would be m - s2/(2t). Many CE Value functions can be computed by evaluating closed form formulas, such as the one just shown for the normal distribution. In other cases, such as for the Beta distribution, use of series expansions is necessary, which are summed until the relative error of the remainder term is sufficiently small. In yet other cases, such as for the lognormal distribution, numerical integration is required to compute the underlying expected utility value.
The function collection is provided as a Windows DLL so that it can be used is Office applications such as EXCEL as well Windows applications written in Visual Basic, C++, Delphi or other language equipped to interface with the Windows API. The probability distributions presently included in the CE-VALUE PAK are shown in the following table, which separates them according to whether the distribution is discrete or continuous. Note that the Histogram Distribution is included in the continuous distribution collection, so that the value of simulated returns may be readily computed and compared amongst several alternatives. For a live demo of some of these value functions, check out the online CE-VALUE CALCULATOR which is implemented using JavaScript functions.
| Continuous
Distributions |
Discrete
Distributions |
| Beta |
Binomial |
| Chi-Square |
Discrete
Uniform |
| Exponential |
Finite
Discrete |
| Erlang |
Geometric |
| Gamma |
Hyper-Geometric |
| Histogram |
Negative
Binomial |
| Inverse
Gamma |
Pascal |
| Laplace |
Poisson |
| Logistic |
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| logNormal |
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| Normal |
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| Rayleigh |
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| Triangular |
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| Uniform |
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| Weibull |
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