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7.4 PHASE TYPE DISTRIBUTIONS A nonnegative random variable T is said to have a phase type (PH) distribution if T is the time until absorption in a nite-state continuous time Markov chain. Neuts (1981) provides an introduction to PH distributions. Assuming that the waiting times between states are exponential, the distribution of T is a generalization of the Erlang distribution, which is gamma with an integer-valued shape parameter. Every exponential random variable is of PH, so that, in practice, exponential waiting times are used to obtain PH distributions. Even the use of mixtures of exponentials leading to hyperexponential or mixed Erlang distributions give highly complicated analytical expressions (cf. Neuts, 1981), so generally, mixtures of exponential distributions that are simple enough to be analytically tractable are assumed. Cox (1955) showed that the absorption time in a nite state Markov process has a rational Laplace transform that can be represented by a series of exponential phases. However, note that the waiting times in a PH distribution are not required to be exponential. It is only analytically convenient if they are. The pervasiveness of the exponential distribution as a basis for deriving PH distributions is so thorough that the Encyclopedia of Statistics entry for PH distributions makes this assumption (cf. Shaked and Shantikumar, 1983).

we were designing our Theme around a blue marble-inspired browser color, we wanted to give these images a blue hue. We opened these images, edited them to be blue, and then saved them. In Figure 5.6, you will notice the structure of the branding area of the browser. Next we move onto editing our first cascading style sheet within this extensive Theme structure. Because we are touching up a Theme instead of creating a new one, we don t have to change this. However, you may find yourself experimenting with different sizes of throbber images. It then will be necessary to change some spacing attributes in your cascading style sheets. We are going to edit the brand.css file located in the /communicator/skin/ subdirectory. In Code Listing 5.2 is the full text of brand.css. We have added some comments into the code to show you where to modify. Our comments are noted by //. Under the #navigator-throbber heading you may notice that it has a XUL binding associated with this throbber. That XUL binding is pulled from /global/skin/globalBindings.xml#throbber. This URL reference tells the browser what type of XUL element the throbber is. If you look at the entry in the XML file as shown in Code Listing 5.3, you will see that the throbber area is simply a collection of XUL widgets. Save all of your files, and you are finished with branding the browser component of our Netscape Navigator theme.

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Also, only about half of the companies examined conduct postinvestment reviews. However, when such reviews do get done, the primary intentions are perceived to be to learn lessons from investment decisions and to improve forecasting. Fewer companies use the reviews to help improve their capital planning process. Ways to Improve Companies with the highest level of satisfaction with their capital planning processes use the following techniques: Treat all proposals consistently. Best-practice companies evaluate all capital spending proposals consistently. That is, they do not approach different kinds of capital investment in different ways. There is no special treatment for strategic investment decisions (i.e., top-down initiatives, as opposed to bottom-up proposals). Assess risks. Sound risk-management principles are an essential component of the capital planning process. Uncertainty risk (e.g., business cycle, commodity prices, foreign exchange, and interest rates) should be assessed using sensitivity/scenario (what-if) analysis. As for implementation risk, companies need to examine whether they are well equipped to deliver the projects. Consider all stakeholders. The capital planning process should address the wants and needs of multiple stakeholders, not just those of shareholders. Use nonfinancial measures. Factors such as customer satisfaction, employee attrition, and market share should be used along with traditional financial factors to support proposals. Expand breadth. The breadth of what is included in the capital planning process should be expanded, to include such elements as brand investment and other intangibles. Do a postaudit. Significantly more of the best-practice companies tend to conduct postinvestment reviews: 78% of these companies always or usually do them, as opposed to just 50% of the rest.

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