Question

What is SIMULATION ?

What is the advantage of a simulation?

What is a DISCRETE DISTRIBUTION, give an example?

What is a SYMMETRIC versus SKEWED DISTRIBUTION, give an example?

What is a BOUNDED versus UNBOUNDED DISTRIBUTION, give an example?

Answer 1

What is SIMULATION ?

Simulations (and models, too) are abstractions of reality. Often they deliberately emphasize one part of reality at the expense of other parts. Sometimes this is necessary due to computer power limitations. Sometimes it's done to focus your attention on an important aspect of the simulation. Whereas models are mathematical, logical, or some other structured representation of reality, simulations are the specific application of models to arrive at some outcome

Three types of simulations
Simulations generally come in three styles: live, virtual and constructive. A simulation also may be a combination of two or more styles. Within these styles, simulations can be science-based (where, for example, interactions of things are observed or measured), or involve interactions with humans. Our primary focus at IST is on the latter— human-in-the-loop —simulations.

Live simulations typically involve humans and/or equipment and activity in a setting where they would operate for real. Think war games with soldiers out in the field or manning command posts. Time is continuous, as in the real world. Another example of live simulation is testing a car battery using an electrical tester.

Virtual simulations typically involve humans and/or equipment in a computer-controlled setting. Time is in discrete steps, allowing users to concentrate on the important stuff, so to speak. A flight simulator falls into this category.

Constructive simulations typically do not involve humans or equipment as participants. Rather than by time, they are driven more by the proper sequencing of events. The anticipated path of a hurricane might be "constructed" through application of temperatures, pressures, wind currents and other weather factors. Science-based simulations are typically constructive in nature.

2.

Advantages of Simulation

One of the primary advantages of simulators is that they are able to provide users with practical feedback when designing real world systems. This allows the designer to determine the correctness and efficiency of a design before the system is actually constructed. Consequently, the user may explore the merits of alternative designs without actually physically building the systems. By investigating the effects of specific design decisions during the design phase rather than the construction phase, the overall cost of building the system diminishes significantly. As an example, consider the design and fabrication of integrated circuits. During the design phase, the designer is presented with a myriad of decisions regarding such things as the placement of components and the routing of the connecting wires. It would be very costly to actually fabricate all of the potential designs as a means of evaluating their respective performance. Through the use of a simulator, however, the user may investigate the relative superiority of each design without actually fabricating the circuits themselves. By mimicking the behaviour of the designs, the circuit simulator is able to provide the designer with information pertaining to the correctness and efficiency of alternate designs. After carefully weighing the ramifications of each design, the best circuit may then be fabricated.

Another benefit of simulators is that they permit system designers to study a problem at several different levels of abstraction. By approaching a system at a higher level of abstraction, the designer is better able to understand the behaviours and interactions of all the high level components within the system and is therefore better equipped to counteract the complexity of the overall system. This complexity may simply overwhelm the designer if the problem had been approached from a lower level.

3.What is a DISCRETE DISTRIBUTION, give an example

A discrete distribution is a function that gives the probabilities of observable (either finite or countably infinite) pre-defined values. Unlike a continuous distribution, which probabilistically describes observable outcomes that can take any value in a continuous interval (uncountably infinite) range, a discrete distribution defines probabilities for distinct potential outcomes that do not cover any continuous interval range. Discrete distributions are frequently used in statistical modeling and computer programming.

An example of a discrete distribution: rolling two dice and recording each of the probabilities of the sum being 2, 3, 4, etc., up to 12.

A business world example: a railroad company recording probabilities of various equipment or service failures on a particular route over a particular time interval. This discrete distribution could assist the company in allocating resources to address these issues.

4.What is a SYMMETRIC versus SKEWED DISTRIBUTION, give an example

5.What is a BOUNDED versus UNBOUNDED DISTRIBUTION, give an example

A distribution that is confined to lie between two determined values is said to be bounded. A distribution that is unbounded theoretically extends from minus infinity to plus infinity. A distribution that is constrained at one or either end is said to be partially bounded. Unbounded and partially bounded distributions may, at times, need to be constrained to remove the tail of the distribution so that nonsensical values are avoided. For example, using a Normal distribution to model sales volume opens up the chance of generating a negative value. If the probability of generating a negative value is significant, and we want to stick to using a Normal distribution, we must constrain the model in some way to eliminate any negative sales volume figure being generated.

• Some distributions are intrinsically bounded -- samples are guaranteed to lie between a known minimum and maximum value. Examples are the Uniform, Triangular, Beta, and Binomial distributions.
• Other distributions are unbounded -- sample values may cluster around the distribution’s mean, but may sometimes have extreme negative or positive values. Examples are the Normal, Logistic, and Extreme Value distributions.
• Still other distributions are partially bounded, with a known minimum such as zero, but no maximum value. Examples are the Exponential, Poisson, and Weibull distributions.

At times, you may find that the most appropriate distribution (say the Normal) is unbounded, but you know that the realistic values of the physical process are bounded, or your model is designed to handle values only up to some realistic limit. Your software may allow you to truncate an unbounded distribution. For example, in Risk Solver you can impose bounds on any distribution by passing the PsiTruncate property function as an argument to the distribution function.