# Question

Although the normal distribution is a reasonable input distribution in many situations, it does have two potential drawbacks:

(1) It allows negative values, even though they may be extremely improbable, and

(2) It is a symmetric distribution.

Many situations are modeled better with a distribution that allows only positive values and is skewed to the right. Two of these that have been used in many real applications are the gamma and lognormal distributions. @RISK enables you to generate observations from each of these distributions.

The @RISK function for the gamma distribution is RISKGAMMA, and it takes two arguments, as in =RISKGAMMA(3,10). The first argument, which must be positive, determines the shape. The smaller it is, the more skewed the distribution is to the right; the larger it is, the more symmetric the distribution is. The second argument determines the scale, in the sense that the product of it and the first argument equals the mean of the distribution. Also, the product of the second argument and the square root of the first argument is the standard deviation of the distribution. The @RISK function for the lognormal distribution is RISKLOGNORM. It has two arguments, as in =RISKLOGNORM(40,10).

These arguments are the mean and standard deviation of the distribution. Rework Example 15.2 for the following demand distributions. Do the simulated outputs have any different qualitative properties with these skewed distributions than with the triangular distribution used in the example?

a. Gamma distribution with parameters 2 and 85

b. Gamma distribution with parameters 5 and 35

c. Lognormal distribution with mean 170 and standard deviation 60

(1) It allows negative values, even though they may be extremely improbable, and

(2) It is a symmetric distribution.

Many situations are modeled better with a distribution that allows only positive values and is skewed to the right. Two of these that have been used in many real applications are the gamma and lognormal distributions. @RISK enables you to generate observations from each of these distributions.

The @RISK function for the gamma distribution is RISKGAMMA, and it takes two arguments, as in =RISKGAMMA(3,10). The first argument, which must be positive, determines the shape. The smaller it is, the more skewed the distribution is to the right; the larger it is, the more symmetric the distribution is. The second argument determines the scale, in the sense that the product of it and the first argument equals the mean of the distribution. Also, the product of the second argument and the square root of the first argument is the standard deviation of the distribution. The @RISK function for the lognormal distribution is RISKLOGNORM. It has two arguments, as in =RISKLOGNORM(40,10).

These arguments are the mean and standard deviation of the distribution. Rework Example 15.2 for the following demand distributions. Do the simulated outputs have any different qualitative properties with these skewed distributions than with the triangular distribution used in the example?

a. Gamma distribution with parameters 2 and 85

b. Gamma distribution with parameters 5 and 35

c. Lognormal distribution with mean 170 and standard deviation 60

## Answer to relevant Questions

The Fizzy Company produces six-packs of soda cans. Each can is supposed to contain at least 12 ounces of soda. If the total weight in a six-pack is less than 72 ounces, Fizzy is fined $100 and receives no sales revenue for ...The effect of the shapes of input distributions on the distribution of an output can depend on the output function. For this problem, assume there are 10 input variables. The goal is to compare the case where these 10 inputs ...Assume that all of a company’s job applicants must take a test, and that the scores on this test are normally distributed. The selection ratio is the cutoff point used by the company in its hiring process. For example, a ...We are continually hearing reports on the nightly news about natural disasters—droughts in Texas, hurricanes in Florida, floods in California, and so on. We often hear that one of these was the “worst in over 30 ...In the cash balance model from Example 16.5, is the $250,000 minimum cash balance requirement really “costing” the company very much? Answer this by rerunning the simulation with minimum required cash balances of ...Post your question

0