This is a wonderful resource for anyone considering the use of Monte Carlo simulation methodology in SAS. Curran, Ph. Although the book is written at a fairly basic level, it skillfully previews many of the underlying statistical theories necessary for understanding the techniques discussed. Marcoulides, Ph. Convert currency. Add to Basket. Condition: New. Seller Inventory NEW More information about this seller Contact this seller. Condition: Brand New. Seller Inventory A Never used!.
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Buy with confidence, excellent customer service!. Seller Inventory n. Xitao Fan Ph. Publisher: SAS Institute , This specific ISBN edition is currently not available. View all copies of this ISBN edition:. Synopsis About this title With the advance of computing technology, Monte Carlo simulation research has become increasingly popular among quantitative researchers in a variety of disciplines. About the Author : Xitao Fan, Ph.
Review : Although accessible to a wide range of SAS users, even experienced users will learn clever new tricks for data generation, management and analysis. Buy New Learn more about this copy. Customers who bought this item also bought. Stock Image. The male random population possesses identical characteristics not shown here. The logarithm of weight is also normally distributed, and it is highly correlated with height. In Chapter 4, we will demonstrate how to generate multivariate random variables with a given degree of correlation.
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N Sum Weights Mean Kolmogorov-Smirnov D 0. Knowing the negative answer in advance, it also calculates the logarithm of the price and finds that to be normal. The stock prices in many other months follow different distributions.
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A variable is lognormally distributed if its logarithm is normally distributed. If the lognormal distribution has a mean of m and a standard deviation of s, then the variable PRICE in the statement below will follow lognormal distribution.
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The histogram of the random sample closely follows the theoretical curve. The histogram gets much smoother and closer to the theoretical one when we increase the sample size to , The program rounds the generated prices in two ways. Or when the theoretical distribution is unknown and we only possess a stepwise approximation of it, RANTBL is the generator of choice again. Variable r receives a value of. If we need different values to be generated, we have to map 1,2, The following two methods result in the same random numbers:.
As mentioned earlier, the following solutions provide the same results, but take a little less time to execute because we leave out the last probability:. The execution time of the RANTBL function, in general, increases linearly with the number of probabilities specified, and it does not depend on the above two methods. Then we pretend that the lognormal distribution in Section 3.
This example generates a sample portfolio of 10, bonds following the rating composition of U.
In Moody's bond rating scale, 'Aaa' indicates the lowest level of risk, 'Aa' the second lowest level of risk and 'Caa' including 'Ca' and 'C' the highest. The heart of the program is the statement. This program determines what the ideal composition of the portfolio would be in a sample of 10, bonds, and compares the random sample to this one using the chi- square test.
The non-significant result of the chi-square test p-value of 0. Let us assume that the stock prices in the example in Section 3. The program finally determines the cumulative distribution function of the random stock prices and plots it along with the theoretical one. The closeness of the two curves is clear in Figure 3.
The first ten randomly generated values are shown in Output 3. Set up a sample identifier. When we create more than one random variable, the CALL form should be used with carefully picked seed values in order to avoid overlapping or correlated streams of random numbers. Various SAS procedures help verify the distribution of the generated random numbers. Fishman, G. Hamer, R. Killam, B. Knuth, D. Reading, MA: Addison-Wesley. Lehmer, F. Cambridge: Harvard University Press. Bond Rating Distribution. Ralston, A.
Encyclopedia of Computer Science. New York: Van Nostrand Reinhold. Rubinstein, R. Simulation and the Monte Carlo Method. Bureau of the Census. This chapter is a continuation of that discussion. To conduct a Monte Carlo study, it is obviously necessary to generate sample data in such a fashion that the generated sample data adequately represent random samples from a population with known population characteristics, such as population central tendency e.
Furthermore, population characteristics also include whether or not the population is normally distributed, and in the case of non-normal distributions, the nature and degree of non-normality e. When the analysis involves more than one variable, as is usually the case in most analysis situations, not only individual variable distribution characteristics i. Fundamentally, the validity of any Monte Carlo study results hinges on the adequacy of data generation, both for individual variables and for inter-variable relationship patterns.
The purpose of this chapter is to present procedures for data generation, and to present SAS program examples to implement the data generation procedures. The theoretical aspects of data generation are briefly covered when necessary to provide readers with the necessary theoretical underpinnings of the data generation procedures. SAS programming examples of data generation are provided for all important aspects of data generation so that readers will be able to apply these data generation procedures in SAS in their own work. But we must be able to generate samples of a single variable before we can attempt to tackle the situation involving multiple variables.
This section discusses how such a task can be accomplished in SAS. Simulating data as if they were sampled from a standard normal distribution—i. So the major focus of this chapter is on generating sample data for a population with a known degree of non-normality. Because many statistical analyses assume data normality, the impact of violating data normality assumption on the validity of statistical results often becomes an area of focus for empirical investigations. Consequently, data non- normality is often one important area of research interest in Monte Carlo simulation studies.
The numerical values obtained through repeated generation of the SAS normal variate generator RANNOR can be considered as z scores from a normally distributed Z score distribution, which is used widely in many statistical analyses. To linearly transform normally distributed data to a new distribution with the desired population mean and variance requires only a simple linear transformation. Linear transformation only changes the mean and variance of a distribution, but not the shape of the distribution as defined by the distribution's third and fourth statistical moments i. The formula used for such linear transformation is as follows:.