Question

Why are conditional test procedures an integral part of statistics? Provide a real world example using pseudocode.

Answer 1

The study of probability distributions of economic variables is an important subject and has a long history, for example, the study of income distribution by Pareto (1897) and that of wealth distribution by Sargan (1957). In financial economics, the distributions of assets’ returns have been extensively examined, e.g., Fama (1967). In risk management, the distribution of a portfolio’s value is closely monitored by asset managers. Often undertaken in econometrics is testing distributional assumptions, with a usual focus on normality, as in Bera and Jarque (1982). This paper studies the problem of testing conditional distributions of dynamic models, where distributions evolve over time. Though not a focus of this paper, dynamic conditional distributions is related to density forecasting, which is a major concern in risk management. For further elaboration on this topic, see Diebold, Gunther and Tay (1998).

EXAMPLE

An algorithm is a procedure for solving a problem in terms of the actions to be executed and the order in which those actions are to be executed. An algorithm is merely the sequence of steps taken to solve a problem. The steps are normally "sequence," "selection, " "iteration," and a case-type statement.

In C, "sequence statements" are imperatives. The "selection" is the "if then else" statement, and the iteration is satisfied by a number of statements, such as the "while," " do," and the "for," while the case-type statement is satisfied by the "switch" statement.

Pseudocode is an artificial and informal language that helps programmers develop algorithms. Pseudocode is a "text-based" detail (algorithmic) design tool.

The rules of Pseudocode are reasonably straightforward. All statements showing "dependency" are to be indented. These include while, do, for, if, switch. Examples below will illustrate this notion.

Examples:

1.. If student's grade is greater than or equal to 60

• Print "passed"

else

• Print "failed"

2. Set total to zero

Set grade counter to one

While grade counter is less than or equal to ten

• Input the next grade

• Add the grade into the total

Set the class average to the total divided by ten

Print the class average.

3.

Initialize total to zero

Initialize counter to zero

Input the first grade

while the user has not as yet entered the sentinel

• add this grade into the running total

• add one to the grade counter

• input the next grade (possibly the sentinel)

if the counter is not equal to zero

• set the average to the total divided by the counter

• print the average

else

• print 'no grades were entered'

4.

initialize passes to zero

initialize failures to zero

initialize student to one

while student counter is less than or equal to ten

• input the next exam result

• if the student passed < >add one to passes add one to failures

add one to student counter

print the number of passes

print the number of failures

if eight or more students passed

• print "raise tuition"

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