A Review of Activity Time Distributions in Risk Analysis <s> 6) The Triangular Distribution <s> This paper presents the results of a mathematical analysis of the standard assumptions used in PERT calculations. The objectives of this analysis were four-fold: 1 to pull together the mathematical aspects of the PERT model, 2 to suggest relevant analytic techniques, 3 to obtain an indication of the magnitude and direction of errors introduced by the assumptions, and 4 to suggest possible modifications and improvements in the model. The first part of the paper analyzes those assumptions relevant to the individual activities. Three possible sources of error are considered here: 1 the beta distribution assumption, 2 the standard deviation assumption and the approximation formula for the mean, and 3 the imprecise time estimates. The second part of the paper deals with the PERT network as a whole and analyzes the calculations underlying the project mean, standard deviation, and probability statements. The concept of relative criticalness is explored for the PERT stochastic model. Techniques for network reduction are outlined. <s> BIB001 </s> A Review of Activity Time Distributions in Risk Analysis <s> 6) The Triangular Distribution <s> This paper introduces a new probability distribution referred to as a transformed triangular ::: distribution (TTD) by using the average of the extreme values (minimum and maximum) of the ::: triangular distribution. The TTD is being approximated by the continuous uniform distribution. ::: The basic moments of the TTD and those of the continuous uniform distribution are compared ::: respectively, and a relationship established. This can be used in modeling and simulation. <s> BIB002
The triangular distribution has also been suggested as a priori distribution for activity times. Mac Crimmon and Ryavec BIB001 and Elmaghraby  earlier suggested that the triangular distribution could be considered as activity time distribution. The triangular distribution can be symmetric, positive or negative skewed. A random variable X with triangular distribution has the probability density function, ( ) 2 ; x a a x m b a m a g See Hajdu and Bokor  and Okagbue, et al. BIB002 for more on triangular distribution. recursive method, using two extreme points, a and b to be supplied by the expert. Their method followed after SANs technique. They opined that this method has an advantage over some activity task distributions with point estimates.