China
Africa
Explore chapters and articles related to this topic
Probability Distributions
Published in Alan R. Jones, Probability, Statistics and Other Frightening Stuff, 2018
However, for lower values of α and β there are some notable exceptions to the generic ‘distended bell’ curves, as illustrated in Figure 4.18. These occur when either parameter equals one or less: When both α = 1 and β = 1, we will generate an Open Interval Continuous Uniform Distribution.When one parameter equals one and the other equals two, we will get a right-angled Triangular Distribution i.e. one where the Mode equals either the Minimum or Maximum value.When both α and β are less than one (but greater than zero), we can generate some bizarre bimodal distributions (or 'washing lines'). So, if we are going to guess the values of parameters α and β (OK, let me rephrase, that. . .) So, if we are going to make an 'uninformed judgement' on the values of parameters α and β, we should avoid selecting values this low. In a practical situation where we may be creating a simulation model we may want to restrict the model parameters to higher values to avoid such unintended outcomes.
Principles of Economic Mine Closure, Reclamation and Cost Management
Published in M.H. Wong, J.W.C. Wong, A.J.M. Baker, Remediation and Management of Degraded Lands, 2018
Table 14.2 lists the distributions and parameters for quantities as well as unit rates. For recontouring, a triangular distribution is assumed for the quantity of earthworks. The triangular distribution has a minimum value of 180,000 m3, a maximum value of 220,000 m3, and a mean value of 200,000 m3. The unit cost is assumed to follow a normal distribution with a mean value of $0.38 and a standard deviation of $0.08. After performing the Monte Carlo simulation, the probabilistic results for the cost estimate shown in Figure 14.3 are obtained. These results show that when using expected values for all parameters, the predicted value for closure costs is $139,700 (the results shown in Table 14.1). However, there is a 10% probability that the closure cost will exceed $163,700 or that it will be smaller than $116,900. By using this approach, the potential high and low ends of the cost estimate can be identified, and this can be used by management as a decision-making tool for funds to be set aside for closure.
Randomness
Published in Raymond J. Madachy, Daniel X. Houston, What Every Engineer Should Know About Modeling and Simulation, 2017
Raymond J. Madachy, Daniel X. Houston
Probability distributions are based on independent, random values. The total area under a probability distribution function (PDF) is unity. Distributions may be continuous or they can be discrete. Frequency histograms of data values are also probability distributions. The integral, or cumulative form of the PDF is called the cumulative distribution function (CDF). A common application of the cumulative distribution is to generate random variates using the inverse transform method.Common probability distributions for modeling systems include the following simple ones:Uniform distribution represents a range of equally likely values.Triangular distribution is specified with a minimum, maximum, and most likely value.Normal distribution is a bell-shaped symmetric distribution defined by its mean and standard deviation.Lognormal distribution is a positively skewed continuous distribution.Gamma distribution is right-skewed and can take on various shapes defined by its constants.
On the Quotient of Extreme Order Statistics from Two Triangularly Distributed Random Variables
Published in American Journal of Mathematical and Management Sciences, 2021
The triangular distribution is useful for modeling the uncertainty restricted within some domain, and especially when difficulty occurs in collecting data due to nature or high costs. The parameters a, m and b may be identified by a lower estimate a most likely estimate and an upper estimate of a characteristic under consideration. When the form of the underlying distribution is unknown, but a minimal value some maximal value and a most likely value of a characteristic are available, then the distribution is recommended. For example, in PERT (Project Evaluation and Review Technique) this characteristic is the completion time of an activity in a project. As another example, when one searches the size of an underground reservoir in oil or gas exploration, he/she performs three tests to obtain the three point estimates.
Ethanol production from food waste in West Attica: evaluation of investment plans under uncertainty
Published in Biofuels, 2020
A. Konti, P. Papagiannakopoulou, D. Mamma, D. Kekos, D. Damigos
Some of the most commonly used distributions are: Uniform distribution: it defines only the minimum and maximum values of the possible range of values of the uncertain parameter. It is used when there is no information available about the frequency of occurrence of in-between values.Triangular distribution: used when in addition to a range a most likely value or midpoint is known.Standard distribution: assumes a standard deviation from a given mean value.Other characteristic distributions are the normal, gamma, beta, Weibull, and logarithmic distributions for specific cases of uncertainty [21].
Performance-based contract design under cost uncertainty: A scenario-based bilevel programming approach
Published in The Engineering Economist, 2018
Mohammadreza Sharifi, Roy H. Kwon
Each scenario is represented by the vector of uncertain values of (Cm,Cr,k). We assume that all three cost variables follow triangular distributions. We also generated 10 outliers to represent the extreme events, shaping the tail of the cost distribution. The parameters of the triangular distribution are shown as a vector (min, mode, max). The values for the triangular parameters of the cost variables are presented in Table 6. We can observe that the maximum values can be up to three times the mode values, which is due to high uncertainty and unpredictability of the costs. Because the values of the cost variables are independent of each other, we can assume a joint distribution of all of these factors and represent them in one vector for each scenario.