Guide to COST-BENEFIT ANALYSIS of investment projects - Ramiri

The degree of dispersion of the possible values around the mean is measured by the standard deviation 130Figure H.2 Gaussian distribution1.000.750.500.250.000.20% 0.30% 0.40% 0.50% 0.60% 0.70%Normal distributions occur in a lot of different situations. When there is reason to suspect the presence of a largenumber of small effects acting additively and independently, it is reasonable to assume that observations will benormally distributed.Triangular or three-point distributions are often used when there is no detailed information on the variable’s pastbehaviour. This simple distribution is completely described by a ‘High Value’, a ‘Low Value’ and the ‘Best-GuessValue’, which, respectively, provide the maximum, the minimum and the modal values of the probability distribution.Triangular Distribution is typically used as a subjective description of a population for which there is only limitedsample data, and especially in cases where the relationship between variables is known but data is scarce (possiblybecause of the high cost of collection). The precise analytical and graphical specification of a triangular distributionvaries a lot, depending on the weight given to the modal value in relation to the extreme point values.Figure H.3 Symmetric and asymmetric triangular distributions0.15600.10400.05200.000 5 10 15 20 25Productivity index0-2.00% -1.00% 0.00% 1.00% 2.00% 3.00%Accrual/year of real wage growthThe diagrams in figure H. 3 show two types of triangular distributions:- the first one is symmetric, with the high value as likely as the low ones and with the same range between themodal value and the low value and between the modal value and the high value;- the second one is asymmetric, with the high value more likely than the low ones and with a larger range betweenthe modal value and the high value than the range between the modal value and the low value (or vice-versa).If there is no reason to believe that within a range a given value is more likely to materialise than others, thedistribution obtained is called Uniform, i.e. a distribution for which all intervals of the same length on thedistribution’s support are equally probable.1302( t −t)−22σ(1f x)= eσ 2πwith − ∞ < x < ∞235